TSTP Solution File: ITP166^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP166^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:04:24 EDT 2024
% Result : Theorem 0.15s 0.55s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 483
% Syntax : Number of formulae : 957 ( 328 unt; 253 typ; 0 def)
% Number of atoms : 6653 (1072 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 1255 ( 460 ~; 384 |; 101 &; 0 @)
% ( 111 <=>; 199 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 1069 (1068 >; 1 *; 0 +; 0 <<)
% Number of symbols : 315 ( 312 usr; 120 con; 0-8 aty)
% Number of variables : 1536 ( 12 ^1370 !; 139 ?;1536 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
bexp: $tType ).
thf(type_def_6,type,
list_char: $tType ).
thf(type_def_7,type,
int: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_9,type,
set_list_typerep: $tType ).
thf(type_def_10,type,
typerep: $tType ).
thf(type_def_11,type,
list_typerep: $tType ).
thf(type_def_12,type,
set_typerep: $tType ).
thf(type_def_13,type,
set_Pr1148378109ar_int: $tType ).
thf(type_def_14,type,
produc1260470173ar_int: $tType ).
thf(type_def_15,type,
com: $tType ).
thf(type_def_16,type,
nat: $tType ).
thf(type_def_17,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_18,type,
set_nat: $tType ).
thf(type_def_19,type,
set_Pr1333062727ar_int: $tType ).
thf(type_def_20,type,
aexp: $tType ).
thf(type_def_21,type,
product_prod_nat_nat: $tType ).
thf(type_def_22,type,
list_nat: $tType ).
thf(type_def_23,type,
set_Pr1560408065st_nat: $tType ).
thf(type_def_24,type,
set_Pr1097818217yperep: $tType ).
thf(type_def_25,type,
set_Pr446800905yperep: $tType ).
thf(type_def_26,type,
list_P1741976099ar_int: $tType ).
thf(type_def_27,type,
set_li1762364675ar_int: $tType ).
thf(type_def_28,type,
produc1699244961st_nat: $tType ).
thf(type_def_29,type,
produc490010537yperep: $tType ).
thf(type_def_30,type,
produc1346207591ar_int: $tType ).
thf(type_def_31,type,
produc1788831497yperep: $tType ).
thf(type_def_32,type,
literal: $tType ).
thf(func_def_0,type,
set_Pr1333062727ar_int: $tType ).
thf(func_def_1,type,
produc1346207591ar_int: $tType ).
thf(func_def_2,type,
set_li1762364675ar_int: $tType ).
thf(func_def_3,type,
set_Pr446800905yperep: $tType ).
thf(func_def_4,type,
list_P1741976099ar_int: $tType ).
thf(func_def_5,type,
set_Pr1148378109ar_int: $tType ).
thf(func_def_6,type,
set_Pr1560408065st_nat: $tType ).
thf(func_def_7,type,
produc490010537yperep: $tType ).
thf(func_def_8,type,
produc1260470173ar_int: $tType ).
thf(func_def_9,type,
produc1699244961st_nat: $tType ).
thf(func_def_10,type,
set_Pr1097818217yperep: $tType ).
thf(func_def_11,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_12,type,
produc1788831497yperep: $tType ).
thf(func_def_13,type,
product_prod_nat_nat: $tType ).
thf(func_def_14,type,
set_list_typerep: $tType ).
thf(func_def_15,type,
list_typerep: $tType ).
thf(func_def_16,type,
set_typerep: $tType ).
thf(func_def_17,type,
list_char: $tType ).
thf(func_def_18,type,
list_nat: $tType ).
thf(func_def_19,type,
set_nat: $tType ).
thf(func_def_20,type,
typerep: $tType ).
thf(func_def_21,type,
literal: $tType ).
thf(func_def_22,type,
bexp: $tType ).
thf(func_def_23,type,
aexp: $tType ).
thf(func_def_24,type,
nat: $tType ).
thf(func_def_25,type,
int: $tType ).
thf(func_def_26,type,
com: $tType ).
thf(func_def_27,type,
bval: bexp > ( list_char > int ) > $o ).
thf(func_def_28,type,
bNF_Gr457912949yperep: set_list_typerep > typerep > set_list_typerep ).
thf(func_def_29,type,
bNF_Gr1303086585yperep: set_list_typerep > list_typerep > set_typerep ).
thf(func_def_30,type,
bNF_Gr202451329ar_int: set_Pr1148378109ar_int > ( produc1260470173ar_int > com ) > ( produc1260470173ar_int > list_char > int ) > set_Pr1148378109ar_int ).
thf(func_def_31,type,
bNF_Gr749752805at_nat: set_Pr1148378109ar_int > ( produc1260470173ar_int > nat ) > ( produc1260470173ar_int > nat ) > set_Pr1986765409at_nat ).
thf(func_def_32,type,
bNF_Gr1247133574at_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_33,type,
bNF_Gr808751971at_nat: set_nat > set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
thf(func_def_34,type,
bNF_Gr1143394412nt_nat: set_Pr1148378109ar_int > set_Pr1986765409at_nat > ( produc1260470173ar_int > nat ) > set_Pr1333062727ar_int ).
thf(func_def_35,type,
big_big_step: produc1260470173ar_int > ( list_char > int ) > $o ).
thf(func_def_36,type,
assign: list_char > aexp > com ).
thf(func_def_37,type,
if: bexp > com > com > com ).
thf(func_def_38,type,
skip: com ).
thf(func_def_39,type,
seq: com > com > com ).
thf(func_def_40,type,
while: bexp > com > com ).
thf(func_def_41,type,
size_com: com > nat ).
thf(func_def_42,type,
unique1592618082ux_nat: product_prod_nat_nat > $o ).
thf(func_def_43,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_44,type,
zero_zero_nat: nat ).
thf(func_def_45,type,
append_nat: list_nat > list_nat > list_nat ).
thf(func_def_46,type,
append_typerep: list_typerep > list_typerep > list_typerep ).
thf(func_def_47,type,
gen_length_typerep: nat > list_typerep > nat ).
thf(func_def_48,type,
lex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
thf(func_def_49,type,
lex_typerep: set_Pr1097818217yperep > set_Pr446800905yperep ).
thf(func_def_50,type,
lexord_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
thf(func_def_51,type,
lexord_typerep: set_Pr1097818217yperep > set_Pr446800905yperep ).
thf(func_def_52,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_53,type,
cons_P1254790739ar_int: produc1260470173ar_int > list_P1741976099ar_int > list_P1741976099ar_int ).
thf(func_def_54,type,
cons_typerep: typerep > list_typerep > list_typerep ).
thf(func_def_55,type,
size_list_typerep: ( typerep > nat ) > list_typerep > nat ).
thf(func_def_56,type,
listrel1_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
thf(func_def_57,type,
listrel1_typerep: set_Pr1097818217yperep > set_Pr446800905yperep ).
thf(func_def_58,type,
set_Co1954412371ar_int: set_Pr1148378109ar_int > set_li1762364675ar_int > set_li1762364675ar_int ).
thf(func_def_59,type,
set_Cons_typerep: set_typerep > set_list_typerep > set_list_typerep ).
thf(func_def_60,type,
suc: nat > nat ).
thf(func_def_61,type,
size_size_com: com > nat ).
thf(func_def_62,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_63,type,
size_s416147576yperep: list_typerep > nat ).
thf(func_def_64,type,
size_size_typerep: typerep > nat ).
thf(func_def_65,type,
produc1193801173ar_int: com > ( list_char > int ) > produc1260470173ar_int ).
thf(func_def_66,type,
produc1625736153st_nat: list_nat > list_nat > produc1699244961st_nat ).
thf(func_def_67,type,
produc1695567329yperep: list_typerep > list_typerep > produc490010537yperep ).
thf(func_def_68,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_69,type,
produc317451735ar_int: produc1260470173ar_int > produc1260470173ar_int > produc1346207591ar_int ).
thf(func_def_70,type,
produc2071514689yperep: typerep > typerep > produc1788831497yperep ).
thf(func_def_71,type,
relati186416454e_flip: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( list_char > int ) > ( list_char > int ) > $o ).
thf(func_def_72,type,
relati23543761ar_int: ( ( list_char > int ) > ( list_char > int ) > $o ) > bexp > com > nat > ( list_char > int ) > ( list_char > int ) > $o ).
thf(func_def_73,type,
relati2102071307_hoare: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
thf(func_def_74,type,
relati775585786_valid: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
thf(func_def_75,type,
collec672902542ar_int: ( list_P1741976099ar_int > $o ) > set_li1762364675ar_int ).
thf(func_def_76,type,
collect_list_typerep: ( list_typerep > $o ) > set_list_typerep ).
thf(func_def_77,type,
collec770796680ar_int: ( produc1260470173ar_int > $o ) > set_Pr1148378109ar_int ).
thf(func_def_78,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_79,type,
collec1834387154ar_int: ( produc1346207591ar_int > $o ) > set_Pr1333062727ar_int ).
thf(func_def_80,type,
typerep2: literal > list_typerep > typerep ).
thf(func_def_81,type,
size_typerep: typerep > nat ).
thf(func_def_82,type,
member2052091212ar_int: list_P1741976099ar_int > set_li1762364675ar_int > $o ).
thf(func_def_83,type,
member_list_typerep: list_typerep > set_list_typerep > $o ).
thf(func_def_84,type,
member_nat: nat > set_nat > $o ).
thf(func_def_85,type,
member92250950ar_int: produc1260470173ar_int > set_Pr1148378109ar_int > $o ).
thf(func_def_86,type,
member1926390090st_nat: produc1699244961st_nat > set_Pr1560408065st_nat > $o ).
thf(func_def_87,type,
member1812711762yperep: produc490010537yperep > set_Pr446800905yperep > $o ).
thf(func_def_88,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_89,type,
member100911538yperep: produc1788831497yperep > set_Pr1097818217yperep > $o ).
thf(func_def_90,type,
member_typerep: typerep > set_typerep > $o ).
thf(func_def_91,type,
p: ( list_char > int ) > ( list_char > int ) > $o ).
thf(func_def_92,type,
q: ( list_char > int ) > ( list_char > int ) > $o ).
thf(func_def_93,type,
b: bexp ).
thf(func_def_94,type,
c: com ).
thf(func_def_95,type,
c2: com ).
thf(func_def_96,type,
k: nat ).
thf(func_def_97,type,
ka: nat ).
thf(func_def_98,type,
s: list_char > int ).
thf(func_def_99,type,
s_a: list_char > int ).
thf(func_def_100,type,
s2: list_char > int ).
thf(func_def_101,type,
sa: list_char > int ).
thf(func_def_102,type,
t: list_char > int ).
thf(func_def_103,type,
t_a: list_char > int ).
thf(func_def_104,type,
t2: list_char > int ).
thf(func_def_105,type,
ta: list_char > int ).
thf(func_def_106,type,
u: list_char > int ).
thf(func_def_107,type,
ua: list_char > int ).
thf(func_def_111,type,
vAND: $o > $o > $o ).
thf(func_def_112,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_113,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_114,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_115,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_116,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_117,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_118,type,
vIMP: $o > $o > $o ).
thf(func_def_119,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_120,type,
vOR: $o > $o > $o ).
thf(func_def_121,type,
vNOT: $o > $o ).
thf(func_def_122,type,
sP0: ( com > $o ) > $o ).
thf(func_def_123,type,
sP1: ( com > $o ) > $o ).
thf(func_def_124,type,
sP2: ( list_char > int ) > bexp > com > ( list_char > int ) > $o ).
thf(func_def_125,type,
sP3: ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > nat > bexp > com > ( list_char > int ) > com > ( list_char > int ) > $o ).
thf(func_def_126,type,
sK4: com > bexp ).
thf(func_def_127,type,
sK5: com > com ).
thf(func_def_128,type,
sK6: com > bexp ).
thf(func_def_129,type,
sK7: com > com ).
thf(func_def_130,type,
sK8: com > com ).
thf(func_def_131,type,
sK9: com > com ).
thf(func_def_132,type,
sK10: com > com ).
thf(func_def_133,type,
sK11: com > list_char ).
thf(func_def_134,type,
sK12: com > aexp ).
thf(func_def_135,type,
sK13: nat > nat ).
thf(func_def_136,type,
sK14: nat > nat ).
thf(func_def_137,type,
sK15: product_prod_nat_nat > nat ).
thf(func_def_138,type,
sK16: product_prod_nat_nat > nat ).
thf(func_def_139,type,
sK17: produc1260470173ar_int > com ).
thf(func_def_140,type,
sK18: produc1260470173ar_int > list_char > int ).
thf(func_def_141,type,
sK19: product_prod_nat_nat > nat ).
thf(func_def_142,type,
sK20: product_prod_nat_nat > nat ).
thf(func_def_143,type,
sK21: produc1260470173ar_int > com ).
thf(func_def_144,type,
sK22: produc1260470173ar_int > list_char > int ).
thf(func_def_145,type,
sK23: set_Pr1986765409at_nat > nat ).
thf(func_def_146,type,
sK24: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_147,type,
sK25: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_148,type,
sK26: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_149,type,
sK27: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_150,type,
sK28: ( produc1260470173ar_int > $o ) > com ).
thf(func_def_151,type,
sK29: ( produc1260470173ar_int > $o ) > list_char > int ).
thf(func_def_152,type,
sK30: ( produc1260470173ar_int > $o ) > com ).
thf(func_def_153,type,
sK31: ( produc1260470173ar_int > $o ) > list_char > int ).
thf(func_def_154,type,
sK32: ( nat > $o ) > nat ).
thf(func_def_155,type,
sK33: ( nat > $o ) > nat ).
thf(func_def_156,type,
sK34: ( com > $o ) > bexp ).
thf(func_def_157,type,
sK35: ( com > $o ) > com ).
thf(func_def_158,type,
sK36: ( com > $o ) > com ).
thf(func_def_159,type,
sK37: ( com > $o ) > com ).
thf(func_def_160,type,
sK38: ( com > $o ) > com ).
thf(func_def_161,type,
sK39: ( com > $o ) > bexp ).
thf(func_def_162,type,
sK40: ( com > $o ) > com ).
thf(func_def_163,type,
sK41: ( com > $o ) > list_char ).
thf(func_def_164,type,
sK42: ( com > $o ) > aexp ).
thf(func_def_165,type,
sK43: ( nat > $o ) > nat ).
thf(func_def_166,type,
sK44: ( nat > nat > $o ) > nat ).
thf(func_def_167,type,
sK45: ( nat > nat > $o ) > nat ).
thf(func_def_168,type,
sK46: ( nat > nat > $o ) > nat ).
thf(func_def_169,type,
sK47: ( nat > nat > $o ) > nat ).
thf(func_def_170,type,
sK48: ( nat > nat > $o ) > nat ).
thf(func_def_171,type,
sK49: ( nat > nat > $o ) > nat ).
thf(func_def_172,type,
sK50: ( nat > nat > $o ) > nat ).
thf(func_def_173,type,
sK51: ( nat > nat > $o ) > nat ).
thf(func_def_174,type,
sK52: ( nat > nat > $o ) > nat ).
thf(func_def_175,type,
sK53: com > com > list_char > int ).
thf(func_def_176,type,
sK54: com > com > list_char > int ).
thf(func_def_177,type,
sK55: com > com > list_char > int ).
thf(func_def_178,type,
sK56: com > com > list_char > int ).
thf(func_def_179,type,
sK57: com > com > list_char > int ).
thf(func_def_180,type,
sK58: com > com > list_char > int ).
thf(func_def_181,type,
sK59: set_Pr1986765409at_nat > nat ).
thf(func_def_182,type,
sK60: set_Pr1986765409at_nat > nat ).
thf(func_def_183,type,
sK61: com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_184,type,
sK62: com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_185,type,
sK63: com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_186,type,
sK64: com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_187,type,
sK65: set_Pr1097818217yperep > typerep ).
thf(func_def_188,type,
sK66: set_Pr1986765409at_nat > nat ).
thf(func_def_189,type,
sK67: set_Pr1097818217yperep > list_typerep > typerep > list_typerep > list_typerep ).
thf(func_def_190,type,
sK68: set_Pr1097818217yperep > list_typerep > typerep > list_typerep > typerep ).
thf(func_def_191,type,
sK69: set_Pr1097818217yperep > list_typerep > list_typerep > typerep > list_typerep ).
thf(func_def_192,type,
sK70: set_Pr1097818217yperep > list_typerep > list_typerep > typerep > typerep ).
thf(func_def_193,type,
sK71: set_Pr1986765409at_nat > list_nat > nat > list_nat > list_nat ).
thf(func_def_194,type,
sK72: set_Pr1986765409at_nat > list_nat > nat > list_nat > nat ).
thf(func_def_195,type,
sK73: set_Pr1986765409at_nat > list_nat > list_nat > nat > list_nat ).
thf(func_def_196,type,
sK74: set_Pr1986765409at_nat > list_nat > list_nat > nat > nat ).
thf(func_def_197,type,
sK75: ( list_char > int ) > bexp > com > ( list_char > int ) > list_char > int ).
thf(func_def_198,type,
sK76: ( list_char > int ) > ( list_char > int ) > com > com > list_char > int ).
thf(func_def_199,type,
sK77: com > bexp > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > nat ).
thf(func_def_200,type,
sK78: com > bexp > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > nat ).
thf(func_def_201,type,
sK79: com > com > list_char > int ).
thf(func_def_202,type,
sK80: com > com > list_char > int ).
thf(func_def_203,type,
sK81: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_204,type,
sK82: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_205,type,
sK83: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_206,type,
sK84: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_207,type,
sK85: ( list_char > int ) > ( list_char > int ) > list_char > int ).
thf(func_def_208,type,
sK86: ( list_char > int ) > ( list_char > int ) > list_char > int ).
thf(func_def_209,type,
sK87: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_210,type,
sK88: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_211,type,
sK89: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_212,type,
sK90: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_213,type,
sK91: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_214,type,
sK92: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_215,type,
sK93: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_216,type,
sK94: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_217,type,
sK95: ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > nat > bexp > com > ( list_char > int ) > com > ( list_char > int ) > list_char > int ).
thf(func_def_218,type,
sK96: ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > nat > bexp > com > ( list_char > int ) > com > ( list_char > int ) > list_char > int ).
thf(func_def_219,type,
sK97: com > ( ( list_char > int ) > ( list_char > int ) > $o ) > com > bexp > nat > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_220,type,
sK98: com > ( ( list_char > int ) > ( list_char > int ) > $o ) > com > bexp > nat > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_221,type,
sK99: com > bexp > nat > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > nat ).
thf(func_def_222,type,
sK100: com > bexp > nat > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_223,type,
sK101: com > bexp > nat > ( nat > ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_225,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_226,type,
sK103: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(func_def_227,type,
sK104: nat > list_typerep > list_typerep ).
thf(func_def_228,type,
sK105: list_typerep > nat > list_typerep ).
thf(f2663,plain,
$false,
inference(avatar_sat_refutation,[],[f1601,f1605,f1638,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1691,f1695,f1700,f1705,f1709,f1714,f1719,f1723,f1727,f1731,f1735,f1740,f1744,f1748,f1752,f1756,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1833,f1838,f1842,f1847,f1852,f1856,f1860,f1864,f1868,f1872,f1876,f1880,f1884,f1888,f1893,f1898,f1903,f1908,f1960,f1964,f1968,f2008,f2012,f2016,f2020,f2043,f2047,f2057,f2061,f2065,f2076,f2081,f2085,f2089,f2109,f2113,f2119,f2123,f2127,f2131,f2135,f2154,f2286,f2292,f2296,f2390,f2401,f2405,f2409,f2417,f2424,f2476,f2500,f2504,f2508,f2518,f2523,f2529,f2542,f2546,f2552,f2557,f2585,f2589,f2593,f2608,f2612,f2616,f2620,f2624,f2628,f2655,f2662]) ).
thf(f2662,plain,
( ~ spl102_57
| ~ spl102_18
| ~ spl102_55
| ~ spl102_75
| ~ spl102_111 ),
inference(avatar_split_clause,[],[f2661,f2652,f2111,f1895,f1702,f1905]) ).
thf(f1905,plain,
( spl102_57
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_57])]) ).
thf(f1702,plain,
( spl102_18
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_18])]) ).
thf(f1895,plain,
( spl102_55
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_55])]) ).
thf(f2111,plain,
( spl102_75
<=> ! [X0: list_char > int,X1: list_char > int] :
( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X1)),t_a) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X0)),ta) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_75])]) ).
thf(f2652,plain,
( spl102_111
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_111])]) ).
thf(f2661,plain,
( ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) != $true )
| ~ spl102_18
| ~ spl102_55
| ~ spl102_75
| ~ spl102_111 ),
inference(trivial_inequality_removal,[],[f2660]) ).
thf(f2660,plain,
( ( $true != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) != $true )
| ~ spl102_18
| ~ spl102_55
| ~ spl102_75
| ~ spl102_111 ),
inference(forward_demodulation,[],[f2659,f1897]) ).
thf(f1897,plain,
( ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) = $true )
| ~ spl102_55 ),
inference(avatar_component_clause,[],[f1895]) ).
thf(f2659,plain,
( ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) != $true )
| ~ spl102_18
| ~ spl102_75
| ~ spl102_111 ),
inference(trivial_inequality_removal,[],[f2658]) ).
thf(f2658,plain,
( ( $true != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) != $true )
| ~ spl102_18
| ~ spl102_75
| ~ spl102_111 ),
inference(forward_demodulation,[],[f2657,f1704]) ).
thf(f1704,plain,
( ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa) = $true )
| ~ spl102_18 ),
inference(avatar_component_clause,[],[f1702]) ).
thf(f2657,plain,
( ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa) != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) != $true )
| ~ spl102_75
| ~ spl102_111 ),
inference(trivial_inequality_removal,[],[f2656]) ).
thf(f2656,plain,
( ( $true != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa) != $true )
| ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) != $true )
| ~ spl102_75
| ~ spl102_111 ),
inference(superposition,[],[f2112,f2654]) ).
thf(f2654,plain,
( ( vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true )
| ~ spl102_111 ),
inference(avatar_component_clause,[],[f2652]) ).
thf(f2112,plain,
( ! [X0: list_char > int,X1: list_char > int] :
( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X0)),ta) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X1)),t_a) ) )
| ~ spl102_75 ),
inference(avatar_component_clause,[],[f2111]) ).
thf(f2655,plain,
spl102_111,
inference(avatar_split_clause,[],[f1144,f2652]) ).
thf(f1144,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true,
inference(cnf_transformation,[],[f504]) ).
thf(f504,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true,
inference(fool_elimination,[],[f503]) ).
thf(f503,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Suc_Oprems_I7_J) ).
thf(f2628,plain,
spl102_110,
inference(avatar_split_clause,[],[f1164,f2626]) ).
thf(f2626,plain,
( spl102_110
<=> ! [X4: list_nat,X0: nat,X5: list_nat,X2: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_110])]) ).
thf(f1164,plain,
! [X2: set_Pr1986765409at_nat,X0: nat,X1: nat,X4: list_nat,X5: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(equality_resolution,[],[f1163]) ).
thf(f1163,plain,
! [X2: set_Pr1986765409at_nat,X3: list_nat,X0: nat,X1: nat,X4: list_nat,X5: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X3),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(equality_resolution,[],[f1124]) ).
thf(f1124,plain,
! [X2: set_Pr1986765409at_nat,X3: list_nat,X0: nat,X1: nat,X6: list_nat,X4: list_nat,X5: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X3),X6)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)) != X6 )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f733]) ).
thf(f733,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat,X6: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X3),X6)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)) != X6 )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(flattening,[],[f732]) ).
thf(f732,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat,X6: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X3),X6)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)) != X6 )
| ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f476]) ).
thf(f476,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat,X6: list_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) )
=> ( ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5)) = X3 )
=> ( ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)) = X6 )
=> ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X3),X6)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) ) ) ) ),
inference(fool_elimination,[],[f475]) ).
thf(f475,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat,X6: list_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2)
=> ( ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X5)) = X3 )
=> ( ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X4),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)) = X6 )
=> vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X3),X6)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) ) ) ),
inference(rectify,[],[f215]) ).
thf(f215,axiom,
! [X53: nat,X46: nat,X128: set_Pr1986765409at_nat,X129: list_nat,X141: list_nat,X142: list_nat,X134: list_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X53),X46)),X128)
=> ( ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X141),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X53),X142)) = X129 )
=> ( ( vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X141),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X46),X142)) = X134 )
=> vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X129),X134)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X128)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_listrel1I) ).
thf(f2624,plain,
spl102_109,
inference(avatar_split_clause,[],[f1162,f2622]) ).
thf(f2622,plain,
( spl102_109
<=> ! [X4: list_typerep,X0: typerep,X5: list_typerep,X2: set_Pr1097818217yperep,X1: typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_109])]) ).
thf(f1162,plain,
! [X2: set_Pr1097818217yperep,X0: typerep,X1: typerep,X4: list_typerep,X5: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(equality_resolution,[],[f1161]) ).
thf(f1161,plain,
! [X2: set_Pr1097818217yperep,X3: list_typerep,X0: typerep,X1: typerep,X4: list_typerep,X5: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X3),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(equality_resolution,[],[f1123]) ).
thf(f1123,plain,
! [X2: set_Pr1097818217yperep,X3: list_typerep,X0: typerep,X1: typerep,X6: list_typerep,X4: list_typerep,X5: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X3),X6)),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)) != X6 )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f731]) ).
thf(f731,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep,X6: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X3),X6)),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)) != X6 )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(flattening,[],[f730]) ).
thf(f730,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep,X6: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X3),X6)),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)) != X6 )
| ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5)) != X3 )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f474]) ).
thf(f474,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep,X6: list_typerep] :
( ( $true = vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) )
=> ( ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5)) = X3 )
=> ( ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)) = X6 )
=> ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X3),X6)),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) ) ) ) ),
inference(fool_elimination,[],[f473]) ).
thf(f473,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep,X6: list_typerep] :
( vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2)
=> ( ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X5)) = X3 )
=> ( ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X4),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)) = X6 )
=> vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X3),X6)),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) ) ) ),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
! [X53: typerep,X46: typerep,X128: set_Pr1097818217yperep,X129: list_typerep,X141: list_typerep,X142: list_typerep,X134: list_typerep] :
( vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X53),X46)),X128)
=> ( ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X141),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X53),X142)) = X129 )
=> ( ( vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X141),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X46),X142)) = X134 )
=> vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,X129),X134)),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X128)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_listrel1I) ).
thf(f2620,plain,
spl102_108,
inference(avatar_split_clause,[],[f1099,f2618]) ).
thf(f2618,plain,
( spl102_108
<=> ! [X3: list_nat,X4: list_nat,X0: nat,X5: list_nat,X2: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_108])]) ).
thf(f1099,plain,
! [X2: set_Pr1986765409at_nat,X3: list_nat,X0: nat,X1: nat,X4: list_nat,X5: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f707]) ).
thf(f707,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f442]) ).
thf(f442,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) )
=> ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X2)) ) ),
inference(fool_elimination,[],[f441]) ).
thf(f441,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat,X4: list_nat,X5: list_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2)
=> vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X4))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X3),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X5)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X2)) ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X6: nat,X7: nat,X128: set_Pr1986765409at_nat,X11: list_nat,X53: list_nat,X46: list_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X6),X7)),X128)
=> vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X11),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X6),X53))),vAPP(list_nat,list_nat,vAPP(list_nat,sTfun(list_nat,list_nat),append_nat,X11),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X7),X46)))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X128)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_lexord__append__left__rightI) ).
thf(f2616,plain,
spl102_107,
inference(avatar_split_clause,[],[f1549,f2614]) ).
thf(f2614,plain,
( spl102_107
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_107])]) ).
thf(f1549,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( zero_zero_nat = X0 ) ),
inference(equality_proxy_clausification,[],[f1548]) ).
thf(f1548,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0) ) ),
inference(binary_proxy_clausification,[],[f1546]) ).
thf(f1546,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(equality_proxy_clausification,[],[f1545]) ).
thf(f1545,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ) ),
inference(binary_proxy_clausification,[],[f931]) ).
thf(f931,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(cnf_transformation,[],[f266]) ).
thf(f266,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X0)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1)) ),
inference(fool_elimination,[],[f265]) ).
thf(f265,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) )
= ( zero_zero_nat = X1 ) )
& ( zero_zero_nat = X0 ) ),
inference(rectify,[],[f131]) ).
thf(f131,axiom,
! [X53: nat,X46: nat] :
( ( ( zero_zero_nat = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X53),X46) )
= ( zero_zero_nat = X46 ) )
& ( zero_zero_nat = X53 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_zero__eq__add__iff__both__eq__0) ).
thf(f2612,plain,
spl102_106,
inference(avatar_split_clause,[],[f1098,f2610]) ).
thf(f2610,plain,
( spl102_106
<=> ! [X3: list_typerep,X4: list_typerep,X0: typerep,X5: list_typerep,X2: set_Pr1097818217yperep,X1: typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X4))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,lexord_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_106])]) ).
thf(f1098,plain,
! [X2: set_Pr1097818217yperep,X3: list_typerep,X0: typerep,X1: typerep,X4: list_typerep,X5: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X4))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,lexord_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f706]) ).
thf(f706,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X4))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,lexord_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f440]) ).
thf(f440,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep] :
( ( $true = vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) )
=> ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X4))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,lexord_typerep,X2)) ) ),
inference(fool_elimination,[],[f439]) ).
thf(f439,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep,X4: list_typerep,X5: list_typerep] :
( vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2)
=> vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X4))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X3),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X5)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,lexord_typerep,X2)) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X6: typerep,X7: typerep,X128: set_Pr1097818217yperep,X11: list_typerep,X53: list_typerep,X46: list_typerep] :
( vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X6),X7)),X128)
=> vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X11),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X6),X53))),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X11),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X7),X46)))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,lexord_typerep,X128)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_lexord__append__left__rightI) ).
thf(f2608,plain,
spl102_105,
inference(avatar_split_clause,[],[f968,f2606]) ).
thf(f2606,plain,
( spl102_105
<=> ! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK39,X0)),vAPP(sTfun(com,$o),com,sK40,X0))) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list_char,sK41,X0)),vAPP(sTfun(com,$o),aexp,sK42,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_105])]) ).
thf(f968,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK39,X0)),vAPP(sTfun(com,$o),com,sK40,X0))) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list_char,sK41,X0)),vAPP(sTfun(com,$o),aexp,sK42,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(cnf_transformation,[],[f788]) ).
thf(f788,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK39,X0)),vAPP(sTfun(com,$o),com,sK40,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK40,X0)) ) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list_char,sK41,X0)),vAPP(sTfun(com,$o),aexp,sK42,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41,sK42])],[f785,f787,f786]) ).
thf(f786,plain,
! [X0: com > $o] :
( ? [X2: bexp,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) ) )
=> ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK39,X0)),vAPP(sTfun(com,$o),com,sK40,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK40,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f787,plain,
! [X0: com > $o] :
( ? [X4: list_char,X5: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X4),X5)) )
=> ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list_char,sK41,X0)),vAPP(sTfun(com,$o),aexp,sK42,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f785,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X2: bexp,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) ) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ? [X4: list_char,X5: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X4),X5)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(rectify,[],[f740]) ).
thf(f740,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X9: bexp,X10: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
& ( $true = vAPP(com,$o,X0,X10) ) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ? [X2: list_char,X3: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X2),X3)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(definition_folding,[],[f619,f739,f738]) ).
thf(f738,plain,
! [X0: com > $o] :
( ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f739,plain,
! [X0: com > $o] :
( ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f619,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X9: bexp,X10: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
& ( $true = vAPP(com,$o,X0,X10) ) )
| ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ? [X2: list_char,X3: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X2),X3)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(flattening,[],[f618]) ).
thf(f618,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X9: bexp,X10: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
& ( $true = vAPP(com,$o,X0,X10) ) )
| ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ? [X2: list_char,X3: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X2),X3)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(ennf_transformation,[],[f312]) ).
thf(f312,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,skip) )
=> ( ! [X2: list_char,X3: aexp] : ( $true = vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X2),X3)) )
=> ( ! [X4: com,X5: com] :
( ( $true = vAPP(com,$o,X0,X4) )
=> ( ( $true = vAPP(com,$o,X0,X5) )
=> ( $true = vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) ) ) )
=> ( ! [X6: bexp,X7: com,X8: com] :
( ( $true = vAPP(com,$o,X0,X7) )
=> ( ( $true = vAPP(com,$o,X0,X8) )
=> ( $true = vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) ) ) )
=> ( ! [X9: bexp,X10: com] :
( ( $true = vAPP(com,$o,X0,X10) )
=> ( $true = vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) ) )
=> ( $true = vAPP(com,$o,X0,X1) ) ) ) ) ) ),
inference(fool_elimination,[],[f311]) ).
thf(f311,plain,
! [X0: com > $o,X1: com] :
( vAPP(com,$o,X0,skip)
=> ( ! [X2: list_char,X3: aexp] : vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X2),X3))
=> ( ! [X4: com,X5: com] :
( vAPP(com,$o,X0,X4)
=> ( vAPP(com,$o,X0,X5)
=> vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) ) )
=> ( ! [X6: bexp,X7: com,X8: com] :
( vAPP(com,$o,X0,X7)
=> ( vAPP(com,$o,X0,X8)
=> vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) ) )
=> ( ! [X9: bexp,X10: com] :
( vAPP(com,$o,X0,X10)
=> vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
=> vAPP(com,$o,X0,X1) ) ) ) ) ),
inference(rectify,[],[f119]) ).
thf(f119,axiom,
! [X29: com > $o,X107: com] :
( vAPP(com,$o,X29,skip)
=> ( ! [X108: list_char,X109: aexp] : vAPP(com,$o,X29,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X108),X109))
=> ( ! [X108: com,X109: com] :
( vAPP(com,$o,X29,X108)
=> ( vAPP(com,$o,X29,X109)
=> vAPP(com,$o,X29,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X108),X109)) ) )
=> ( ! [X108: bexp,X109: com,X110: com] :
( vAPP(com,$o,X29,X109)
=> ( vAPP(com,$o,X29,X110)
=> vAPP(com,$o,X29,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X108),X109),X110)) ) )
=> ( ! [X108: bexp,X109: com] :
( vAPP(com,$o,X29,X109)
=> vAPP(com,$o,X29,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X108),X109)) )
=> vAPP(com,$o,X29,X107) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_com_Oinduct) ).
thf(f2593,plain,
spl102_104,
inference(avatar_split_clause,[],[f998,f2591]) ).
thf(f2591,plain,
( spl102_104
<=> ! [X2: list_nat,X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK60,X0)),vAPP(set_Pr1986765409at_nat,nat,sK59,X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_104])]) ).
thf(f998,plain,
! [X2: list_nat,X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK60,X0)),vAPP(set_Pr1986765409at_nat,nat,sK59,X0))),X0) ) ),
inference(cnf_transformation,[],[f809]) ).
thf(f809,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat,X2: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK60,X0)),vAPP(set_Pr1986765409at_nat,nat,sK59,X0))),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,sK59,X0) != vAPP(set_Pr1986765409at_nat,nat,sK60,X0) )
& ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK59,X0)),vAPP(set_Pr1986765409at_nat,nat,sK60,X0))),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60])],[f635,f808]) ).
thf(f808,plain,
! [X0: set_Pr1986765409at_nat] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),X0) )
& ( X3 != X4 )
& ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X0) ) )
=> ( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK60,X0)),vAPP(set_Pr1986765409at_nat,nat,sK59,X0))),X0) )
& ( vAPP(set_Pr1986765409at_nat,nat,sK59,X0) != vAPP(set_Pr1986765409at_nat,nat,sK60,X0) )
& ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK59,X0)),vAPP(set_Pr1986765409at_nat,nat,sK60,X0))),X0) ) ) ),
introduced(choice_axiom,[]) ).
thf(f635,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat,X2: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),X0) )
& ( X3 != X4 )
& ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X0) ) ) ),
inference(flattening,[],[f634]) ).
thf(f634,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat,X2: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),X0) )
& ( X3 != X4 )
& ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X0) ) ) ),
inference(ennf_transformation,[],[f328]) ).
thf(f328,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat,X2: list_nat] :
( ! [X3: nat,X4: nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),X0) )
| ( X3 = X4 )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X0) ) )
=> ( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) ) ) ),
inference(fool_elimination,[],[f327]) ).
thf(f327,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat,X2: list_nat] :
( ! [X3: nat,X4: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X4),X3)),X0)
| ( X3 = X4 )
| vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X3),X4)),X0) )
=> ( vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0))
| ( X1 = X2 )
| vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) ) ),
inference(rectify,[],[f200]) ).
thf(f200,axiom,
! [X128: set_Pr1986765409at_nat,X53: list_nat,X46: list_nat] :
( ! [X44: nat,X45: nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X45),X44)),X128)
| ( X44 = X45 )
| vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X44),X45)),X128) )
=> ( vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X46),X53)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X128))
| ( X46 = X53 )
| vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X53),X46)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X128)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_lexord__linear) ).
thf(f2589,plain,
spl102_103,
inference(avatar_split_clause,[],[f996,f2587]) ).
thf(f2587,plain,
( spl102_103
<=> ! [X2: list_nat,X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK59,X0)),vAPP(set_Pr1986765409at_nat,nat,sK60,X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_103])]) ).
thf(f996,plain,
! [X2: list_nat,X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK59,X0)),vAPP(set_Pr1986765409at_nat,nat,sK60,X0))),X0) ) ),
inference(cnf_transformation,[],[f809]) ).
thf(f2585,plain,
spl102_102,
inference(avatar_split_clause,[],[f990,f2583]) ).
thf(f2583,plain,
( spl102_102
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK44,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK45,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X0)),zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_102])]) ).
thf(f990,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK44,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK45,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X0)),zero_zero_nat) ) ),
inference(cnf_transformation,[],[f795]) ).
thf(f795,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK44,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK45,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK44,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK45,X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X0)),zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47])],[f791,f794,f793,f792]) ).
thf(f792,plain,
! [X0: nat > nat > $o] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK44,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK45,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK44,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK45,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f793,plain,
! [X0: nat > nat > $o] :
( ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X5)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK46,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f794,plain,
! [X0: nat > nat > $o] :
( ? [X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero_nat) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK47,X0)),zero_zero_nat) ) ),
introduced(choice_axiom,[]) ).
thf(f791,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
| ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X5)) )
| ? [X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero_nat) ) ),
inference(rectify,[],[f628]) ).
thf(f628,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
| ? [X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4)) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat) ) ),
inference(flattening,[],[f627]) ).
thf(f627,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
| ? [X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4)) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat) ) ),
inference(ennf_transformation,[],[f324]) ).
thf(f324,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat) )
=> ( ! [X4: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4)) )
=> ( ! [X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f323]) ).
thf(f323,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero_nat)
=> ( ! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero_nat),vAPP(nat,nat,suc,X4))
=> ( ! [X5: nat,X6: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ),
inference(rectify,[],[f142]) ).
thf(f142,axiom,
! [X29: nat > nat > $o,X70: nat,X52: nat] :
( ! [X50: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X29,X50),zero_zero_nat)
=> ( ! [X51: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X29,zero_zero_nat),vAPP(nat,nat,suc,X51))
=> ( ! [X50: nat,X51: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X29,X50),X51)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X29,vAPP(nat,nat,suc,X50)),vAPP(nat,nat,suc,X51)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X29,X70),X52) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_diff__induct) ).
thf(f2557,plain,
spl102_101,
inference(avatar_split_clause,[],[f1143,f2554]) ).
thf(f2554,plain,
( spl102_101
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),k),s2),s) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_101])]) ).
thf(f1143,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),k),s2),s) = $true,
inference(cnf_transformation,[],[f502]) ).
thf(f502,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),k),s2),s) = $true,
inference(fool_elimination,[],[f501]) ).
thf(f501,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),k),s2),s),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),k),s2),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062get__back_AP_Ab_Ac_Ak_As_____As_H_____092_060close_062) ).
thf(f2552,plain,
spl102_100,
inference(avatar_split_clause,[],[f1052,f2550]) ).
thf(f2550,plain,
( spl102_100
<=> ! [X0: bexp,X3: list_char > int,X2: list_char > int,X1: com] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X2),X0),X1),X3) )
| ( X2 = X3 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_100])]) ).
thf(f1052,plain,
! [X2: list_char > int,X3: list_char > int,X0: bexp,X1: com] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X2),X0),X1),X3) )
| ( X2 = X3 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) ) ),
inference(cnf_transformation,[],[f742]) ).
thf(f742,plain,
! [X0: bexp,X1: com,X2: list_char > int,X3: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X2),X0),X1),X3) )
| ( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) )
& ( X2 = X3 ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) ) ),
inference(definition_folding,[],[f667,f741]) ).
thf(f741,plain,
! [X3: list_char > int,X1: com,X0: bexp,X2: list_char > int] :
( ( ? [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4) ) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X2),X0),X1),X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f667,plain,
! [X0: bexp,X1: com,X2: list_char > int,X3: list_char > int] :
( ( ? [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4) ) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) ) )
| ( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) )
& ( X2 = X3 ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) ) ),
inference(flattening,[],[f666]) ).
thf(f666,plain,
! [X0: bexp,X1: com,X2: list_char > int,X3: list_char > int] :
( ( ? [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4) ) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) ) )
| ( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) )
& ( X2 = X3 ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) ) ),
inference(ennf_transformation,[],[f588]) ).
thf(f588,plain,
! [X0: bexp,X1: com,X2: list_char > int,X3: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) )
=> ( ( ( X2 = X3 )
=> ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) ) )
=> ~ ( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) )
=> ! [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4) )
=> ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) ) ) ) ) ),
inference(flattening,[],[f376]) ).
thf(f376,plain,
! [X0: bexp,X1: com,X2: list_char > int,X3: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3) )
=> ( ( ( X2 = X3 )
=> ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) ) )
=> ~ ( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) )
=> ! [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4) )
=> ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) ) ) ) ) ),
inference(fool_elimination,[],[f375]) ).
thf(f375,plain,
! [X0: bexp,X1: com,X2: list_char > int,X3: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X2)),X3)
=> ( ( ( X2 = X3 )
=> vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) )
=> ~ ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2)
=> ! [X4: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4)
=> ~ vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X7: bexp,X17: com,X12: list_char > int,X10: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X7),X17)),X12)),X10)
=> ( ( ( X10 = X12 )
=> vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X7),X12) )
=> ~ ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X7),X12)
=> ! [X42: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X17),X12)),X42)
=> ~ vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X7),X17)),X42)),X10) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_WhileE) ).
thf(f2546,plain,
spl102_99,
inference(avatar_split_clause,[],[f1160,f2544]) ).
thf(f2544,plain,
( spl102_99
<=> ! [X2: produc1260470173ar_int,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int,X1: produc1260470173ar_int > com] :
( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,X1,X2)),vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2))),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_99])]) ).
thf(f1160,plain,
! [X2: produc1260470173ar_int,X1: produc1260470173ar_int > com,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,X1,X2)),vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2))),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) ) ),
inference(equality_resolution,[],[f1159]) ).
thf(f1159,plain,
! [X2: produc1260470173ar_int,X0: com,X1: produc1260470173ar_int > com,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2))),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,com,X1,X2) != X0 ) ),
inference(equality_resolution,[],[f1097]) ).
thf(f1097,plain,
! [X2: produc1260470173ar_int,X3: list_char > int,X0: com,X1: produc1260470173ar_int > com,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X3)),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2) != X3 )
| ( vAPP(produc1260470173ar_int,com,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f705]) ).
thf(f705,plain,
! [X0: com,X1: produc1260470173ar_int > com,X2: produc1260470173ar_int,X3: list_char > int,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X3)),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2) != X3 )
| ( vAPP(produc1260470173ar_int,com,X1,X2) != X0 ) ),
inference(flattening,[],[f704]) ).
thf(f704,plain,
! [X0: com,X1: produc1260470173ar_int > com,X2: produc1260470173ar_int,X3: list_char > int,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X3)),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2) != X3 )
| ( vAPP(produc1260470173ar_int,com,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f438]) ).
thf(f438,plain,
! [X0: com,X1: produc1260470173ar_int > com,X2: produc1260470173ar_int,X3: list_char > int,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( vAPP(produc1260470173ar_int,com,X1,X2) = X0 )
=> ( ( vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2) = X3 )
=> ( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
=> ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X3)),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) ) ) ) ),
inference(fool_elimination,[],[f437]) ).
thf(f437,plain,
! [X0: com,X1: produc1260470173ar_int > com,X2: produc1260470173ar_int,X3: list_char > int,X4: produc1260470173ar_int > list_char > int,X5: set_Pr1148378109ar_int] :
( ( vAPP(produc1260470173ar_int,com,X1,X2) = X0 )
=> ( ( vAPP(produc1260470173ar_int,sTfun(list_char,int),X4,X2) = X3 )
=> ( vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5)
=> vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X3)),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X5),X1),X4)) ) ) ),
inference(rectify,[],[f152]) ).
thf(f152,axiom,
! [X7: com,X122: produc1260470173ar_int > com,X53: produc1260470173ar_int,X17: list_char > int,X123: produc1260470173ar_int > list_char > int,X48: set_Pr1148378109ar_int] :
( ( vAPP(produc1260470173ar_int,com,X122,X53) = X7 )
=> ( ( vAPP(produc1260470173ar_int,sTfun(list_char,int),X123,X53) = X17 )
=> ( vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X53),X48)
=> vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X7),X17)),vAPP(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int,vAPP(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,com),sTfun(sTfun(produc1260470173ar_int,sTfun(list_char,int)),set_Pr1148378109ar_int)),bNF_Gr202451329ar_int,X48),X122),X123)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_image2__eqI) ).
thf(f2542,plain,
spl102_98,
inference(avatar_split_clause,[],[f983,f2540]) ).
thf(f2540,plain,
( spl102_98
<=> ! [X2: com,X0: ( list_char > int ) > ( list_char > int ) > $o,X1: bexp] : ( vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,X0),X1),X2),zero_zero_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_98])]) ).
thf(f983,plain,
! [X2: com,X0: ( list_char > int ) > ( list_char > int ) > $o,X1: bexp] : ( vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,X0),X1),X2),zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f565]) ).
thf(f565,plain,
! [X0: ( list_char > int ) > ( list_char > int ) > $o,X1: bexp,X2: com] : ( vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,X0),X1),X2),zero_zero_nat) = X0 ),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
! [X29: ( list_char > int ) > ( list_char > int ) > $o,X7: bexp,X17: com] : ( vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,X29),X7),X17),zero_zero_nat) = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_get__back_Osimps_I1_J) ).
thf(f2529,plain,
spl102_97,
inference(avatar_split_clause,[],[f967,f2527]) ).
thf(f2527,plain,
( spl102_97
<=> ! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK40,X0)) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list_char,sK41,X0)),vAPP(sTfun(com,$o),aexp,sK42,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_97])]) ).
thf(f967,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK40,X0)) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list_char,sK41,X0)),vAPP(sTfun(com,$o),aexp,sK42,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(cnf_transformation,[],[f788]) ).
thf(f2523,plain,
spl102_96,
inference(avatar_split_clause,[],[f1158,f2521]) ).
thf(f2521,plain,
( spl102_96
<=> ! [X2: produc1260470173ar_int,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int,X1: produc1260470173ar_int > nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(produc1260470173ar_int,nat,X1,X2)),vAPP(produc1260470173ar_int,nat,X4,X2))),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_96])]) ).
thf(f1158,plain,
! [X2: produc1260470173ar_int,X1: produc1260470173ar_int > nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(produc1260470173ar_int,nat,X1,X2)),vAPP(produc1260470173ar_int,nat,X4,X2))),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) ) ),
inference(equality_resolution,[],[f1157]) ).
thf(f1157,plain,
! [X2: produc1260470173ar_int,X0: nat,X1: produc1260470173ar_int > nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),vAPP(produc1260470173ar_int,nat,X4,X2))),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,nat,X1,X2) != X0 ) ),
inference(equality_resolution,[],[f1096]) ).
thf(f1096,plain,
! [X2: produc1260470173ar_int,X3: nat,X0: nat,X1: produc1260470173ar_int > nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,nat,X4,X2) != X3 )
| ( vAPP(produc1260470173ar_int,nat,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f703]) ).
thf(f703,plain,
! [X0: nat,X1: produc1260470173ar_int > nat,X2: produc1260470173ar_int,X3: nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,nat,X4,X2) != X3 )
| ( vAPP(produc1260470173ar_int,nat,X1,X2) != X0 ) ),
inference(flattening,[],[f702]) ).
thf(f702,plain,
! [X0: nat,X1: produc1260470173ar_int > nat,X2: produc1260470173ar_int,X3: nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) )
| ( $true != vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
| ( vAPP(produc1260470173ar_int,nat,X4,X2) != X3 )
| ( vAPP(produc1260470173ar_int,nat,X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f436]) ).
thf(f436,plain,
! [X0: nat,X1: produc1260470173ar_int > nat,X2: produc1260470173ar_int,X3: nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( vAPP(produc1260470173ar_int,nat,X1,X2) = X0 )
=> ( ( vAPP(produc1260470173ar_int,nat,X4,X2) = X3 )
=> ( ( $true = vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) ) ) ) ),
inference(fool_elimination,[],[f435]) ).
thf(f435,plain,
! [X0: nat,X1: produc1260470173ar_int > nat,X2: produc1260470173ar_int,X3: nat,X4: produc1260470173ar_int > nat,X5: set_Pr1148378109ar_int] :
( ( vAPP(produc1260470173ar_int,nat,X1,X2) = X0 )
=> ( ( vAPP(produc1260470173ar_int,nat,X4,X2) = X3 )
=> ( vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X2),X5)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X3)),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X5),X1),X4)) ) ) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X7: nat,X122: produc1260470173ar_int > nat,X53: produc1260470173ar_int,X17: nat,X123: produc1260470173ar_int > nat,X48: set_Pr1148378109ar_int] :
( ( vAPP(produc1260470173ar_int,nat,X122,X53) = X7 )
=> ( ( vAPP(produc1260470173ar_int,nat,X123,X53) = X17 )
=> ( vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X53),X48)
=> vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X7),X17)),vAPP(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat,vAPP(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat),vAPP(set_Pr1148378109ar_int,sTfun(sTfun(produc1260470173ar_int,nat),sTfun(sTfun(produc1260470173ar_int,nat),set_Pr1986765409at_nat)),bNF_Gr749752805at_nat,X48),X122),X123)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_image2__eqI) ).
thf(f2518,plain,
spl102_95,
inference(avatar_split_clause,[],[f908,f2516]) ).
thf(f2516,plain,
( spl102_95
<=> ! [X0: ( list_char > int ) > ( list_char > int ) > $o] : ( $true = vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o)),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o))),relati2102071307_hoare,X0),skip),skip),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_95])]) ).
thf(f908,plain,
! [X0: ( list_char > int ) > ( list_char > int ) > $o] : ( $true = vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o)),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o))),relati2102071307_hoare,X0),skip),skip),X0) ),
inference(cnf_transformation,[],[f257]) ).
thf(f257,plain,
! [X0: ( list_char > int ) > ( list_char > int ) > $o] : ( $true = vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o)),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o))),relati2102071307_hoare,X0),skip),skip),X0) ),
inference(fool_elimination,[],[f256]) ).
thf(f256,plain,
! [X0: ( list_char > int ) > ( list_char > int ) > $o] : vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o)),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o))),relati2102071307_hoare,X0),skip),skip),X0),
inference(rectify,[],[f88]) ).
thf(f88,axiom,
! [X29: ( list_char > int ) > ( list_char > int ) > $o] : vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o)),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),$o))),relati2102071307_hoare,X29),skip),skip),X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ir__Skip__Skip) ).
thf(f2508,plain,
spl102_94,
inference(avatar_split_clause,[],[f1030,f2506]) ).
thf(f2506,plain,
( spl102_94
<=> ! [X0: nat,X3: list_nat,X2: set_Pr1986765409at_nat,X1: nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X3)),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X3))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_94])]) ).
thf(f1030,plain,
! [X2: set_Pr1986765409at_nat,X3: list_nat,X0: nat,X1: nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X3)),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X3))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f653]) ).
thf(f653,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X3)),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X3))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) )
| ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f362]) ).
thf(f362,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat] :
( ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2) )
=> ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X3)),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X3))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) ) ),
inference(fool_elimination,[],[f361]) ).
thf(f361,plain,
! [X0: nat,X1: nat,X2: set_Pr1986765409at_nat,X3: list_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X0),X1)),X2)
=> vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X0),X3)),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X1),X3))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X2)) ),
inference(rectify,[],[f207]) ).
thf(f207,axiom,
! [X53: nat,X46: nat,X128: set_Pr1986765409at_nat,X129: list_nat] :
( vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X53),X46)),X128)
=> vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X53),X129)),vAPP(list_nat,list_nat,vAPP(nat,sTfun(list_nat,list_nat),cons_nat,X46),X129))),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,listrel1_nat,X128)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_listrel1I1) ).
thf(f2504,plain,
spl102_93,
inference(avatar_split_clause,[],[f1028,f2502]) ).
thf(f2502,plain,
( spl102_93
<=> ! [X0: typerep,X3: list_typerep,X2: set_Pr1097818217yperep,X1: typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X3)),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X3))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_93])]) ).
thf(f1028,plain,
! [X2: set_Pr1097818217yperep,X3: list_typerep,X0: typerep,X1: typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X3)),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X3))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f650]) ).
thf(f650,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep] :
( ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X3)),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X3))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) )
| ( $true != vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f358]) ).
thf(f358,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep] :
( ( $true = vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2) )
=> ( $true = vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X3)),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X3))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) ) ),
inference(fool_elimination,[],[f357]) ).
thf(f357,plain,
! [X0: typerep,X1: typerep,X2: set_Pr1097818217yperep,X3: list_typerep] :
( vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X0),X1)),X2)
=> vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X3)),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X3))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X2)) ),
inference(rectify,[],[f206]) ).
thf(f206,axiom,
! [X53: typerep,X46: typerep,X128: set_Pr1097818217yperep,X129: list_typerep] :
( vAPP(set_Pr1097818217yperep,$o,vAPP(produc1788831497yperep,sTfun(set_Pr1097818217yperep,$o),member100911538yperep,vAPP(typerep,produc1788831497yperep,vAPP(typerep,sTfun(typerep,produc1788831497yperep),produc2071514689yperep,X53),X46)),X128)
=> vAPP(set_Pr446800905yperep,$o,vAPP(produc490010537yperep,sTfun(set_Pr446800905yperep,$o),member1812711762yperep,vAPP(list_typerep,produc490010537yperep,vAPP(list_typerep,sTfun(list_typerep,produc490010537yperep),produc1695567329yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X53),X129)),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X46),X129))),vAPP(set_Pr1097818217yperep,set_Pr446800905yperep,listrel1_typerep,X128)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_listrel1I1) ).
thf(f2500,plain,
spl102_92,
inference(avatar_split_clause,[],[f997,f2498]) ).
thf(f2498,plain,
( spl102_92
<=> ! [X2: list_nat,X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( vAPP(set_Pr1986765409at_nat,nat,sK59,X0) != vAPP(set_Pr1986765409at_nat,nat,sK60,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_92])]) ).
thf(f997,plain,
! [X2: list_nat,X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X2),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( X1 = X2 )
| ( $true = vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X2)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( vAPP(set_Pr1986765409at_nat,nat,sK59,X0) != vAPP(set_Pr1986765409at_nat,nat,sK60,X0) ) ),
inference(cnf_transformation,[],[f809]) ).
thf(f2476,plain,
spl102_91,
inference(avatar_split_clause,[],[f1032,f2474]) ).
thf(f2474,plain,
( spl102_91
<=> ! [X0: com,X3: list_char > int,X2: list_char > int,X1: list_char > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X3) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_91])]) ).
thf(f1032,plain,
! [X2: list_char > int,X3: list_char > int,X0: com,X1: list_char > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X3) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f657]) ).
thf(f657,plain,
! [X0: com,X1: list_char > int,X2: list_char > int,X3: list_char > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X3) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X2) ) ),
inference(flattening,[],[f656]) ).
thf(f656,plain,
! [X0: com,X1: list_char > int,X2: list_char > int,X3: list_char > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X3) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f366]) ).
thf(f366,plain,
! [X0: com,X1: list_char > int,X2: list_char > int,X3: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X2) )
=> ( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X3) )
=> ( X2 = X3 ) ) ),
inference(fool_elimination,[],[f365]) ).
thf(f365,plain,
! [X0: com,X1: list_char > int,X2: list_char > int,X3: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X2)
=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X0),X1)),X3)
=> ( X2 = X3 ) ) ),
inference(rectify,[],[f47]) ).
thf(f47,axiom,
! [X17: com,X12: list_char > int,X10: list_char > int,X11: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X17),X12)),X10)
=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X17),X12)),X11)
=> ( X10 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_big__step__determ) ).
thf(f2424,plain,
spl102_90,
inference(avatar_split_clause,[],[f982,f2422]) ).
thf(f2422,plain,
( spl102_90
<=> ! [X2: list_typerep,X0: typerep > nat,X1: typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(typerep,nat,X0,X1)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X2))),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_90])]) ).
thf(f982,plain,
! [X2: list_typerep,X0: typerep > nat,X1: typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(typerep,nat,X0,X1)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X2))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f564]) ).
thf(f564,plain,
! [X0: typerep > nat,X1: typerep,X2: list_typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(typerep,nat,X0,X1)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X2))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X53: typerep > nat,X116: typerep,X117: list_typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X53),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X116),X117)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(typerep,nat,X53,X116)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X53),X117))),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_list_Osize__gen_I2_J) ).
thf(f2417,plain,
spl102_89,
inference(avatar_split_clause,[],[f980,f2415]) ).
thf(f2415,plain,
( spl102_89
<=> ! [X2: list_typerep,X0: typerep > nat,X1: list_typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X1)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_89])]) ).
thf(f980,plain,
! [X2: list_typerep,X0: typerep > nat,X1: list_typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X1)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X2)) ),
inference(cnf_transformation,[],[f562]) ).
thf(f562,plain,
! [X0: typerep > nat,X1: list_typerep,X2: list_typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X1)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X0),X2)) ),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X122: typerep > nat,X129: list_typerep,X134: list_typerep] : ( vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X122),vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X129),X134)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X122),X129)),vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,X122),X134)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_size__list__append) ).
thf(f2409,plain,
spl102_88,
inference(avatar_split_clause,[],[f1049,f2407]) ).
thf(f2407,plain,
( spl102_88
<=> ! [X0: list_char > int,X3: list_char > int,X2: bexp,X1: com] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X2),X3) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X3),X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_88])]) ).
thf(f1049,plain,
! [X2: bexp,X3: list_char > int,X0: list_char > int,X1: com] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X2),X3) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X3),X2),X1),X0) ) ),
inference(cnf_transformation,[],[f837]) ).
thf(f837,plain,
! [X0: list_char > int,X1: com,X2: bexp,X3: list_char > int] :
( ( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),vAPP(sTfun(list_char,int),sTfun(list_char,int),vAPP(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int))),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)))),sK75,X3),X2),X1),X0))),X0) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X3)),vAPP(sTfun(list_char,int),sTfun(list_char,int),vAPP(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int))),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)))),sK75,X3),X2),X1),X0)) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X2),X3) ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X3),X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f835,f836]) ).
thf(f836,plain,
! [X0: list_char > int,X1: com,X2: bexp,X3: list_char > int] :
( ? [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),X4)),X0) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X3)),X4) ) )
=> ( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),vAPP(sTfun(list_char,int),sTfun(list_char,int),vAPP(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int))),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)))),sK75,X3),X2),X1),X0))),X0) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X3)),vAPP(sTfun(list_char,int),sTfun(list_char,int),vAPP(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int))),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),sTfun(list_char,int)))),sK75,X3),X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f835,plain,
! [X0: list_char > int,X1: com,X2: bexp,X3: list_char > int] :
( ( ? [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),X4)),X0) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X3)),X4) ) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X2),X3) ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X3),X2),X1),X0) ) ),
inference(rectify,[],[f834]) ).
thf(f834,plain,
! [X3: list_char > int,X1: com,X0: bexp,X2: list_char > int] :
( ( ? [X4: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2)),X4) ) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X2) ) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(com,sTfun(sTfun(list_char,int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o)),vAPP(sTfun(list_char,int),sTfun(bexp,sTfun(com,sTfun(sTfun(list_char,int),$o))),sP2,X2),X0),X1),X3) ) ),
inference(nnf_transformation,[],[f741]) ).
thf(f2405,plain,
spl102_87,
inference(avatar_split_clause,[],[f989,f2403]) ).
thf(f2403,plain,
( spl102_87
<=> ! [X2: com,X0: bexp,X1: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) )
| ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_87])]) ).
thf(f989,plain,
! [X2: com,X0: bexp,X1: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) )
| ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X1) ) ),
inference(cnf_transformation,[],[f626]) ).
thf(f626,plain,
! [X0: bexp,X1: list_char > int,X2: com] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) )
| ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X1) ) ),
inference(ennf_transformation,[],[f569]) ).
thf(f569,plain,
! [X0: bexp,X1: list_char > int,X2: com] :
( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X1) )
=> ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) ) ),
inference(flattening,[],[f322]) ).
thf(f322,plain,
! [X0: bexp,X1: list_char > int,X2: com] :
( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X1) )
=> ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) ) ),
inference(fool_elimination,[],[f321]) ).
thf(f321,plain,
! [X0: bexp,X1: list_char > int,X2: com] :
( ~ vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X0),X1)
=> vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X7: bexp,X12: list_char > int,X17: com] :
( ~ vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,X7),X12)
=> vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X7),X17)),X12)),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_WhileFalse) ).
thf(f2401,plain,
spl102_86,
inference(avatar_split_clause,[],[f952,f2399]) ).
thf(f2399,plain,
( spl102_86
<=> ! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true != vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK23,X0)),vAPP(set_Pr1986765409at_nat,nat,sK23,X0))),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_86])]) ).
thf(f952,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true != vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK23,X0)),vAPP(set_Pr1986765409at_nat,nat,sK23,X0))),X0) ) ),
inference(cnf_transformation,[],[f764]) ).
thf(f764,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true != vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK23,X0)),vAPP(set_Pr1986765409at_nat,nat,sK23,X0))),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f609,f763]) ).
thf(f763,plain,
! [X0: set_Pr1986765409at_nat] :
( ? [X2: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X2)),X0) )
=> ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(set_Pr1986765409at_nat,nat,sK23,X0)),vAPP(set_Pr1986765409at_nat,nat,sK23,X0))),X0) ) ),
introduced(choice_axiom,[]) ).
thf(f609,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ( $true != vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) )
| ? [X2: nat] : ( $true = vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X2)),X0) ) ),
inference(ennf_transformation,[],[f553]) ).
thf(f553,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ! [X2: nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X2)),X0) )
=> ( $true != vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) ) ),
inference(flattening,[],[f298]) ).
thf(f298,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ! [X2: nat] : ( $true != vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X2)),X0) )
=> ( $true != vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) ) ),
inference(fool_elimination,[],[f297]) ).
thf(f297,plain,
! [X0: set_Pr1986765409at_nat,X1: list_nat] :
( ! [X2: nat] : ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X2)),X0)
=> ~ vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X1),X1)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X0)) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X128: set_Pr1986765409at_nat,X129: list_nat] :
( ! [X50: nat] : ~ vAPP(set_Pr1986765409at_nat,$o,vAPP(product_prod_nat_nat,sTfun(set_Pr1986765409at_nat,$o),member701585322at_nat,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X50),X50)),X128)
=> ~ vAPP(set_Pr1560408065st_nat,$o,vAPP(produc1699244961st_nat,sTfun(set_Pr1560408065st_nat,$o),member1926390090st_nat,vAPP(list_nat,produc1699244961st_nat,vAPP(list_nat,sTfun(list_nat,produc1699244961st_nat),produc1625736153st_nat,X129),X129)),vAPP(set_Pr1986765409at_nat,set_Pr1560408065st_nat,lexord_nat,X128)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_lexord__irreflexive) ).
thf(f2390,plain,
spl102_85,
inference(avatar_split_clause,[],[f963,f2388]) ).
thf(f2388,plain,
( spl102_85
<=> ! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK34,X0)),vAPP(sTfun(com,$o),com,sK35,X0)),vAPP(sTfun(com,$o),com,sK36,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_85])]) ).
thf(f963,plain,
! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK34,X0)),vAPP(sTfun(com,$o),com,sK35,X0)),vAPP(sTfun(com,$o),com,sK36,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f780]) ).
thf(f780,plain,
! [X0: com > $o] :
( ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK34,X0)),vAPP(sTfun(com,$o),com,sK35,X0)),vAPP(sTfun(com,$o),com,sK36,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK36,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK35,X0)) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f778,f779]) ).
thf(f779,plain,
! [X0: com > $o] :
( ? [X1: bexp,X2: com,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X1),X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) )
& ( $true = vAPP(com,$o,X0,X2) ) )
=> ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK34,X0)),vAPP(sTfun(com,$o),com,sK35,X0)),vAPP(sTfun(com,$o),com,sK36,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK36,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK35,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f778,plain,
! [X0: com > $o] :
( ? [X1: bexp,X2: com,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X1),X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) )
& ( $true = vAPP(com,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(rectify,[],[f777]) ).
thf(f777,plain,
! [X0: com > $o] :
( ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(nnf_transformation,[],[f739]) ).
thf(f2296,plain,
spl102_84,
inference(avatar_split_clause,[],[f926,f2294]) ).
thf(f2294,plain,
( spl102_84
<=> ! [X0: com,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X0)),vAPP(com,nat,size_size_com,X1))),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_84])]) ).
thf(f926,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X0)),vAPP(com,nat,size_size_com,X1))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f547]) ).
thf(f547,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X0)),vAPP(com,nat,size_size_com,X1))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f173]) ).
thf(f173,axiom,
! [X66: com,X67: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X66),X67)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X66)),vAPP(com,nat,size_size_com,X67))),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_com_Osize_I8_J) ).
thf(f2292,plain,
spl102_83,
inference(avatar_split_clause,[],[f925,f2290]) ).
thf(f2290,plain,
( spl102_83
<=> ! [X0: com,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X0)),vAPP(com,nat,size_com,X1))),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_83])]) ).
thf(f925,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X0)),vAPP(com,nat,size_com,X1))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f546]) ).
thf(f546,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X0)),vAPP(com,nat,size_com,X1))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f163]) ).
thf(f163,axiom,
! [X66: com,X67: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X66),X67)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X66)),vAPP(com,nat,size_com,X67))),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_com_Osize__gen_I3_J) ).
thf(f2286,plain,
spl102_82,
inference(avatar_split_clause,[],[f1003,f2284]) ).
thf(f2284,plain,
( spl102_82
<=> ! [X2: typerep,X0: list_typerep,X1: set_list_typerep] :
( ( $true = vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X2),X0)),X1) )
| ( $true != vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,X0),vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_82])]) ).
thf(f1003,plain,
! [X2: typerep,X0: list_typerep,X1: set_list_typerep] :
( ( $true = vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X2),X0)),X1) )
| ( $true != vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,X0),vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X1),X2)) ) ),
inference(cnf_transformation,[],[f638]) ).
thf(f638,plain,
! [X0: list_typerep,X1: set_list_typerep,X2: typerep] :
( ( $true = vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X2),X0)),X1) )
| ( $true != vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,X0),vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X1),X2)) ) ),
inference(ennf_transformation,[],[f334]) ).
thf(f334,plain,
! [X0: list_typerep,X1: set_list_typerep,X2: typerep] :
( ( $true = vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,X0),vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X1),X2)) )
=> ( $true = vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X2),X0)),X1) ) ),
inference(fool_elimination,[],[f333]) ).
thf(f333,plain,
! [X0: list_typerep,X1: set_list_typerep,X2: typerep] :
( vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,X0),vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X1),X2))
=> vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X2),X0)),X1) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X138: list_typerep,X139: set_list_typerep,X33: typerep] :
( vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,X138),vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X139),X33))
=> vAPP(set_list_typerep,$o,vAPP(list_typerep,sTfun(set_list_typerep,$o),member_list_typerep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X33),X138)),X139) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ShiftD) ).
thf(f2154,plain,
spl102_81,
inference(avatar_split_clause,[],[f1532,f2152]) ).
thf(f2152,plain,
( spl102_81
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_81])]) ).
thf(f1532,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != X0 ) ),
inference(equality_proxy_clausification,[],[f1531]) ).
thf(f1531,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1527]) ).
thf(f1527,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f933]) ).
thf(f933,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
inference(cnf_transformation,[],[f270]) ).
thf(f270,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
inference(fool_elimination,[],[f269]) ).
thf(f269,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 )
= ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f176]) ).
thf(f176,axiom,
! [X7: nat,X6: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X7),X6) = X7 )
= ( zero_zero_nat = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add__0__iff) ).
thf(f2135,plain,
spl102_80,
inference(avatar_split_clause,[],[f976,f2133]) ).
thf(f2133,plain,
( spl102_80
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_80])]) ).
thf(f976,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f558]) ).
thf(f558,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ),
inference(rectify,[],[f108]) ).
thf(f108,axiom,
! [X6: nat,X7: nat,X17: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X6),X7)),X17) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X6),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X7),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add_Oassoc) ).
thf(f2131,plain,
spl102_79,
inference(avatar_split_clause,[],[f975,f2129]) ).
thf(f2129,plain,
( spl102_79
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_79])]) ).
thf(f975,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(cnf_transformation,[],[f557]) ).
thf(f557,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X7: nat,X6: nat,X17: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X6),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X7),X17)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X6),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_add_Oleft__commute) ).
thf(f2127,plain,
spl102_78,
inference(avatar_split_clause,[],[f974,f2125]) ).
thf(f2125,plain,
( spl102_78
<=> ! [X2: list_typerep,X0: set_list_typerep,X1: typerep] : ( vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X0),X1)),X2) = vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_78])]) ).
thf(f974,plain,
! [X2: list_typerep,X0: set_list_typerep,X1: typerep] : ( vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X0),X1)),X2) = vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) ),
inference(cnf_transformation,[],[f556]) ).
thf(f556,plain,
! [X0: set_list_typerep,X1: typerep,X2: list_typerep] : ( vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X0),X1)),X2) = vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X139: set_list_typerep,X33: typerep,X138: list_typerep] : ( vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,vAPP(typerep,set_list_typerep,vAPP(set_list_typerep,sTfun(typerep,set_list_typerep),bNF_Gr457912949yperep,X139),X33)),X138) = vAPP(list_typerep,set_typerep,vAPP(set_list_typerep,sTfun(list_typerep,set_typerep),bNF_Gr1303086585yperep,X139),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X33),X138)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Succ__Shift) ).
thf(f2123,plain,
spl102_77,
inference(avatar_split_clause,[],[f924,f2121]) ).
thf(f2121,plain,
( spl102_77
<=> ! [X0: literal,X1: list_typerep] : ( vAPP(typerep,nat,size_size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_size_typerep),X1)),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_77])]) ).
thf(f924,plain,
! [X0: literal,X1: list_typerep] : ( vAPP(typerep,nat,size_size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_size_typerep),X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f545]) ).
thf(f545,plain,
! [X0: literal,X1: list_typerep] : ( vAPP(typerep,nat,size_size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_size_typerep),X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f185]) ).
thf(f185,axiom,
! [X4: literal,X0: list_typerep] : ( vAPP(typerep,nat,size_size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X4),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_size_typerep),X0)),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_typerep_Osize_I2_J) ).
thf(f2119,plain,
spl102_76,
inference(avatar_split_clause,[],[f923,f2117]) ).
thf(f2117,plain,
( spl102_76
<=> ! [X0: literal,X1: list_typerep] : ( vAPP(typerep,nat,size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_typerep),X1)),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_76])]) ).
thf(f923,plain,
! [X0: literal,X1: list_typerep] : ( vAPP(typerep,nat,size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_typerep),X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f544]) ).
thf(f544,plain,
! [X0: literal,X1: list_typerep] : ( vAPP(typerep,nat,size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_typerep),X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X4: literal,X0: list_typerep] : ( vAPP(typerep,nat,size_typerep,vAPP(list_typerep,typerep,vAPP(literal,sTfun(list_typerep,typerep),typerep2,X4),X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,vAPP(sTfun(typerep,nat),sTfun(list_typerep,nat),size_list_typerep,size_typerep),X0)),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_typerep_Osize__gen) ).
thf(f2113,plain,
spl102_75,
inference(avatar_split_clause,[],[f868,f2111]) ).
thf(f868,plain,
! [X0: list_char > int,X1: list_char > int] :
( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X1)),t_a) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X0)),ta) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ),
inference(cnf_transformation,[],[f597]) ).
thf(f597,plain,
! [X0: list_char > int,X1: list_char > int] :
( ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X1)),t_a) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X0)),ta) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ),
inference(ennf_transformation,[],[f227]) ).
thf(f227,plain,
~ ? [X0: list_char > int,X1: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X1)),t_a) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X0)),ta) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X0) )
& ( $true = vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ),
inference(fool_elimination,[],[f226]) ).
thf(f226,plain,
~ ? [X0: list_char > int,X1: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X1)),t_a)
& vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X0)),ta)
& vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X0)
& vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ),
inference(rectify,[],[f223]) ).
thf(f223,negated_conjecture,
~ ? [X21: list_char > int,X60: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X60)),t_a)
& vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X21)),ta)
& vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X21)
& vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X21),X60) ),
inference(negated_conjecture,[],[f222]) ).
thf(f222,conjecture,
? [X21: list_char > int,X60: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),X60)),t_a)
& vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),X21)),ta)
& vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),X21)
& vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),vAPP(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)))),vAPP(sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o))))),relati23543761ar_int,p),b),c),vAPP(nat,nat,suc,ka)),X21),X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f2109,plain,
spl102_74,
inference(avatar_split_clause,[],[f1530,f2107]) ).
thf(f2107,plain,
( spl102_74
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_74])]) ).
thf(f1530,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) ),
inference(equality_proxy_clausification,[],[f1529]) ).
thf(f1529,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1528]) ).
thf(f1528,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f933]) ).
thf(f2089,plain,
spl102_73,
inference(avatar_split_clause,[],[f956,f2087]) ).
thf(f2087,plain,
( spl102_73
<=> ! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK30,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK31,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_73])]) ).
thf(f956,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK30,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK31,X0))) ) ),
inference(cnf_transformation,[],[f772]) ).
thf(f772,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK30,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK31,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f613,f771]) ).
thf(f771,plain,
! [X0: produc1260470173ar_int > $o] :
( ? [X2: com,X3: list_char > int] : ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3)) )
=> ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK30,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK31,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f613,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ? [X2: com,X3: list_char > int] : ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3)) ) ),
inference(ennf_transformation,[],[f306]) ).
thf(f306,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ! [X2: com,X3: list_char > int] : ( $true = vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3)) )
=> ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f305,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ! [X2: com,X3: list_char > int] : vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3))
=> vAPP(produc1260470173ar_int,$o,X0,X1) ),
inference(rectify,[],[f34]) ).
thf(f34,axiom,
! [X29: produc1260470173ar_int > $o,X43: produc1260470173ar_int] :
( ! [X44: com,X45: list_char > int] : vAPP(produc1260470173ar_int,$o,X29,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X44),X45))
=> vAPP(produc1260470173ar_int,$o,X29,X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_old_Oprod_Oinducts) ).
thf(f2085,plain,
spl102_72,
inference(avatar_split_clause,[],[f955,f2083]) ).
thf(f2083,plain,
( spl102_72
<=> ! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK28,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK29,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_72])]) ).
thf(f955,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK28,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK29,X0))) ) ),
inference(cnf_transformation,[],[f770]) ).
thf(f770,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK28,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK29,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f612,f769]) ).
thf(f769,plain,
! [X0: produc1260470173ar_int > $o] :
( ? [X2: com,X3: list_char > int] : ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3)) )
=> ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(sTfun(produc1260470173ar_int,$o),com,sK28,X0)),vAPP(sTfun(produc1260470173ar_int,$o),sTfun(list_char,int),sK29,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f612,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) )
| ? [X2: com,X3: list_char > int] : ( $true != vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3)) ) ),
inference(ennf_transformation,[],[f304]) ).
thf(f304,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ! [X2: com,X3: list_char > int] : ( $true = vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3)) )
=> ( $true = vAPP(produc1260470173ar_int,$o,X0,X1) ) ),
inference(fool_elimination,[],[f303]) ).
thf(f303,plain,
! [X0: produc1260470173ar_int > $o,X1: produc1260470173ar_int] :
( ! [X2: com,X3: list_char > int] : vAPP(produc1260470173ar_int,$o,X0,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X2),X3))
=> vAPP(produc1260470173ar_int,$o,X0,X1) ),
inference(rectify,[],[f40]) ).
thf(f40,axiom,
! [X29: produc1260470173ar_int > $o,X47: produc1260470173ar_int] :
( ! [X44: com,X45: list_char > int] : vAPP(produc1260470173ar_int,$o,X29,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X44),X45))
=> vAPP(produc1260470173ar_int,$o,X29,X47) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_prod__cases) ).
thf(f2081,plain,
spl102_71,
inference(avatar_split_clause,[],[f1142,f2078]) ).
thf(f2078,plain,
( spl102_71
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_71])]) ).
thf(f1142,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua) = $true,
inference(cnf_transformation,[],[f500]) ).
thf(f500,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua) = $true,
inference(fool_elimination,[],[f499]) ).
thf(f499,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Suc_Oprems_I2_J) ).
thf(f2076,plain,
spl102_70,
inference(avatar_split_clause,[],[f1141,f2073]) ).
thf(f2073,plain,
( spl102_70
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_70])]) ).
thf(f1141,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u) = $true,
inference(cnf_transformation,[],[f498]) ).
thf(f498,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u) = $true,
inference(fool_elimination,[],[f497]) ).
thf(f497,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062_IWHILE_Ab_ADO_Ac_M_At_____J_A_092_060Rightarrow_062_Au_____092_060close_062) ).
thf(f2065,plain,
spl102_69,
inference(avatar_split_clause,[],[f1526,f2063]) ).
thf(f2063,plain,
( spl102_69
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_69])]) ).
thf(f1526,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) != X0 ) ),
inference(equality_proxy_clausification,[],[f1525]) ).
thf(f1525,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) ) ),
inference(equality_proxy_clausification,[],[f1521]) ).
thf(f1521,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f934]) ).
thf(f934,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) ),
inference(cnf_transformation,[],[f272]) ).
thf(f272,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) ),
inference(fool_elimination,[],[f271]) ).
thf(f271,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 )
= ( zero_zero_nat = X1 ) ),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X6: nat,X7: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X7),X6) = X6 )
= ( zero_zero_nat = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_add__cancel__right__left) ).
thf(f2061,plain,
spl102_68,
inference(avatar_split_clause,[],[f1587,f2059]) ).
thf(f2059,plain,
( spl102_68
<=> ! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_68])]) ).
thf(f1587,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ),
inference(forward_demodulation,[],[f979,f926]) ).
thf(f979,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X1)),vAPP(com,nat,size_size_com,X2))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f561]) ).
thf(f561,plain,
! [X0: bexp,X1: com,X2: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X1)),vAPP(com,nat,size_size_com,X2))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f165]) ).
thf(f165,axiom,
! [X83: bexp,X84: com,X85: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X83),X84),X85)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X84)),vAPP(com,nat,size_size_com,X85))),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_com_Osize_I9_J) ).
thf(f2057,plain,
spl102_67,
inference(avatar_split_clause,[],[f1586,f2055]) ).
thf(f2055,plain,
( spl102_67
<=> ! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_67])]) ).
thf(f1586,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ),
inference(forward_demodulation,[],[f978,f925]) ).
thf(f978,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X1)),vAPP(com,nat,size_com,X2))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f560]) ).
thf(f560,plain,
! [X0: bexp,X1: com,X2: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X1)),vAPP(com,nat,size_com,X2))),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f162]) ).
thf(f162,axiom,
! [X83: bexp,X84: com,X85: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X83),X84),X85)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X84)),vAPP(com,nat,size_com,X85))),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_com_Osize__gen_I4_J) ).
thf(f2047,plain,
spl102_66,
inference(avatar_split_clause,[],[f966,f2045]) ).
thf(f2045,plain,
( spl102_66
<=> ! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK37,X0)),vAPP(sTfun(com,$o),com,sK38,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_66])]) ).
thf(f966,plain,
! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK37,X0)),vAPP(sTfun(com,$o),com,sK38,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f784]) ).
thf(f784,plain,
! [X0: com > $o] :
( ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK37,X0)),vAPP(sTfun(com,$o),com,sK38,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK38,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK37,X0)) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f782,f783]) ).
thf(f783,plain,
! [X0: com > $o] :
( ? [X1: com,X2: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) )
& ( $true = vAPP(com,$o,X0,X2) )
& ( $true = vAPP(com,$o,X0,X1) ) )
=> ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK37,X0)),vAPP(sTfun(com,$o),com,sK38,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK38,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK37,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f782,plain,
! [X0: com > $o] :
( ? [X1: com,X2: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) )
& ( $true = vAPP(com,$o,X0,X2) )
& ( $true = vAPP(com,$o,X0,X1) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(rectify,[],[f781]) ).
thf(f781,plain,
! [X0: com > $o] :
( ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(nnf_transformation,[],[f738]) ).
thf(f2043,plain,
spl102_65,
inference(avatar_split_clause,[],[f973,f2041]) ).
thf(f2041,plain,
( spl102_65
<=> ! [X2: list_typerep,X0: nat,X1: typerep] : ( vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) = vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,vAPP(nat,nat,suc,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_65])]) ).
thf(f973,plain,
! [X2: list_typerep,X0: nat,X1: typerep] : ( vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) = vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,vAPP(nat,nat,suc,X0)),X2) ),
inference(cnf_transformation,[],[f555]) ).
thf(f555,plain,
! [X0: nat,X1: typerep,X2: list_typerep] : ( vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,X0),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X1),X2)) = vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,vAPP(nat,nat,suc,X0)),X2) ),
inference(rectify,[],[f196]) ).
thf(f196,axiom,
! [X52: nat,X53: typerep,X129: list_typerep] : ( vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,X52),vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X53),X129)) = vAPP(list_typerep,nat,vAPP(nat,sTfun(list_typerep,nat),gen_length_typerep,vAPP(nat,nat,suc,X52)),X129) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_gen__length__code_I2_J) ).
thf(f2020,plain,
spl102_64,
inference(avatar_split_clause,[],[f971,f2018]) ).
thf(f2018,plain,
( spl102_64
<=> ! [X0: list_char > int,X1: list_char > int] :
( ( X0 = X1 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_64])]) ).
thf(f971,plain,
! [X0: list_char > int,X1: list_char > int] :
( ( X0 = X1 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X1) ) ),
inference(cnf_transformation,[],[f622]) ).
thf(f622,plain,
! [X0: list_char > int,X1: list_char > int] :
( ( X0 = X1 )
| ( $true != vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X1) ) ),
inference(ennf_transformation,[],[f316]) ).
thf(f316,plain,
! [X0: list_char > int,X1: list_char > int] :
( ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X1) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f315]) ).
thf(f315,plain,
! [X0: list_char > int,X1: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X1)
=> ( X0 = X1 ) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X12: list_char > int,X10: list_char > int] :
( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X12)),X10)
=> ( X10 = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_SkipE) ).
thf(f2016,plain,
spl102_63,
inference(avatar_split_clause,[],[f1524,f2014]) ).
thf(f2014,plain,
( spl102_63
<=> ! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_63])]) ).
thf(f1524,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) ),
inference(equality_proxy_clausification,[],[f1523]) ).
thf(f1523,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) ) ),
inference(equality_proxy_clausification,[],[f1522]) ).
thf(f1522,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero_nat),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f934]) ).
thf(f2012,plain,
spl102_62,
inference(avatar_split_clause,[],[f954,f2010]) ).
thf(f2010,plain,
( spl102_62
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK26,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK27,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_62])]) ).
thf(f954,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK26,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK27,X0))) ) ),
inference(cnf_transformation,[],[f768]) ).
thf(f768,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK26,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK27,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f611,f767]) ).
thf(f767,plain,
! [X0: product_prod_nat_nat > $o] :
( ? [X2: nat,X3: nat] : ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3)) )
=> ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK26,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK27,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f611,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ? [X2: nat,X3: nat] : ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3)) ) ),
inference(ennf_transformation,[],[f302]) ).
thf(f302,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ! [X2: nat,X3: nat] : ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3)) )
=> ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) ) ),
inference(fool_elimination,[],[f301]) ).
thf(f301,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ! [X2: nat,X3: nat] : vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3))
=> vAPP(product_prod_nat_nat,$o,X0,X1) ),
inference(rectify,[],[f33]) ).
thf(f33,axiom,
! [X29: product_prod_nat_nat > $o,X43: product_prod_nat_nat] :
( ! [X44: nat,X45: nat] : vAPP(product_prod_nat_nat,$o,X29,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X44),X45))
=> vAPP(product_prod_nat_nat,$o,X29,X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_old_Oprod_Oinducts) ).
thf(f2008,plain,
spl102_61,
inference(avatar_split_clause,[],[f953,f2006]) ).
thf(f2006,plain,
( spl102_61
<=> ! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK24,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK25,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_61])]) ).
thf(f953,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK24,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK25,X0))) ) ),
inference(cnf_transformation,[],[f766]) ).
thf(f766,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK24,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK25,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f610,f765]) ).
thf(f765,plain,
! [X0: product_prod_nat_nat > $o] :
( ? [X2: nat,X3: nat] : ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3)) )
=> ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(sTfun(product_prod_nat_nat,$o),nat,sK24,X0)),vAPP(sTfun(product_prod_nat_nat,$o),nat,sK25,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f610,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) )
| ? [X2: nat,X3: nat] : ( $true != vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3)) ) ),
inference(ennf_transformation,[],[f300]) ).
thf(f300,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ! [X2: nat,X3: nat] : ( $true = vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3)) )
=> ( $true = vAPP(product_prod_nat_nat,$o,X0,X1) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f299,plain,
! [X0: product_prod_nat_nat > $o,X1: product_prod_nat_nat] :
( ! [X2: nat,X3: nat] : vAPP(product_prod_nat_nat,$o,X0,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X2),X3))
=> vAPP(product_prod_nat_nat,$o,X0,X1) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X29: product_prod_nat_nat > $o,X47: product_prod_nat_nat] :
( ! [X44: nat,X45: nat] : vAPP(product_prod_nat_nat,$o,X29,vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X44),X45))
=> vAPP(product_prod_nat_nat,$o,X29,X47) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_prod__cases) ).
thf(f1968,plain,
spl102_60,
inference(avatar_split_clause,[],[f922,f1966]) ).
thf(f1966,plain,
( spl102_60
<=> ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_60])]) ).
thf(f922,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f543]) ).
thf(f543,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f172]) ).
thf(f172,axiom,
! [X55: bexp,X56: com] : ( vAPP(com,nat,size_size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X55),X56)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_size_com,X56)),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_com_Osize_I10_J) ).
thf(f1964,plain,
spl102_59,
inference(avatar_split_clause,[],[f921,f1962]) ).
thf(f1962,plain,
( spl102_59
<=> ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_59])]) ).
thf(f921,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f542]) ).
thf(f542,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f164]) ).
thf(f164,axiom,
! [X55: bexp,X56: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X55),X56)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(com,nat,size_com,X56)),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_com_Osize__gen_I5_J) ).
thf(f1960,plain,
spl102_58,
inference(avatar_split_clause,[],[f920,f1958]) ).
thf(f1958,plain,
( spl102_58
<=> ! [X0: list_typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X0)),vAPP(list_typerep,nat,size_s416147576yperep,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_58])]) ).
thf(f920,plain,
! [X0: list_typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X0)),vAPP(list_typerep,nat,size_s416147576yperep,X1)) ),
inference(cnf_transformation,[],[f541]) ).
thf(f541,plain,
! [X0: list_typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X0)),vAPP(list_typerep,nat,size_s416147576yperep,X1)) ),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
! [X129: list_typerep,X134: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(list_typerep,sTfun(list_typerep,list_typerep),append_typerep,X129),X134)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X129)),vAPP(list_typerep,nat,size_s416147576yperep,X134)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_length__append) ).
thf(f1908,plain,
spl102_57,
inference(avatar_split_clause,[],[f1140,f1905]) ).
thf(f1140,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) = $true,
inference(cnf_transformation,[],[f496]) ).
thf(f496,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta) = $true,
inference(fool_elimination,[],[f495]) ).
thf(f495,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),sa)),ta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Suc_Oprems_I3_J) ).
thf(f1903,plain,
spl102_56,
inference(avatar_split_clause,[],[f1139,f1900]) ).
thf(f1900,plain,
( spl102_56
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),s2)),t2) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_56])]) ).
thf(f1139,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),s2)),t2) = $true,
inference(cnf_transformation,[],[f494]) ).
thf(f494,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),s2)),t2) = $true,
inference(fool_elimination,[],[f493]) ).
thf(f493,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),s2)),t2),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c),s2)),t2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062_Ic_M_As_____J_A_092_060Rightarrow_062_At_____092_060close_062) ).
thf(f1898,plain,
spl102_55,
inference(avatar_split_clause,[],[f1138,f1895]) ).
thf(f1138,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) = $true,
inference(cnf_transformation,[],[f492]) ).
thf(f492,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a) = $true,
inference(fool_elimination,[],[f491]) ).
thf(f491,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Suc_Oprems_I4_J) ).
thf(f1893,plain,
spl102_54,
inference(avatar_split_clause,[],[f1137,f1890]) ).
thf(f1890,plain,
( spl102_54
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s)),t) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_54])]) ).
thf(f1137,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s)),t) = $true,
inference(cnf_transformation,[],[f490]) ).
thf(f490,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s)),t) = $true,
inference(fool_elimination,[],[f489]) ).
thf(f489,plain,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s)),t),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,c2),s)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062_Ic_H_M_As_H_____J_A_092_060Rightarrow_062_At_H_____092_060close_062) ).
thf(f1888,plain,
spl102_53,
inference(avatar_split_clause,[],[f1061,f1886]) ).
thf(f1886,plain,
( spl102_53
<=> ! [X4: com,X0: list_char,X3: com,X2: bexp,X1: aexp] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_53])]) ).
thf(f1061,plain,
! [X2: bexp,X3: com,X0: list_char,X1: aexp,X4: com] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(cnf_transformation,[],[f592]) ).
thf(f592,plain,
! [X0: list_char,X1: aexp,X2: bexp,X3: com,X4: com] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(rectify,[],[f157]) ).
thf(f157,axiom,
! [X116: list_char,X117: aexp,X83: bexp,X84: com,X85: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X83),X84),X85) != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X116),X117) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_com_Odistinct_I11_J) ).
thf(f1884,plain,
spl102_52,
inference(avatar_split_clause,[],[f1060,f1882]) ).
thf(f1882,plain,
( spl102_52
<=> ! [X4: com,X0: com,X3: com,X2: bexp,X1: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_52])]) ).
thf(f1060,plain,
! [X2: bexp,X3: com,X0: com,X1: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(cnf_transformation,[],[f591]) ).
thf(f591,plain,
! [X0: com,X1: com,X2: bexp,X3: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X66: com,X67: com,X83: bexp,X84: com,X85: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X66),X67) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X83),X84),X85) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_com_Odistinct_I15_J) ).
thf(f1880,plain,
spl102_51,
inference(avatar_split_clause,[],[f1059,f1878]) ).
thf(f1878,plain,
( spl102_51
<=> ! [X4: com,X0: bexp,X3: bexp,X2: com,X1: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_51])]) ).
thf(f1059,plain,
! [X2: com,X3: bexp,X0: bexp,X1: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X3),X4) ),
inference(cnf_transformation,[],[f590]) ).
thf(f590,plain,
! [X0: bexp,X1: com,X2: com,X3: bexp,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X3),X4) ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X83: bexp,X84: com,X85: com,X55: bexp,X56: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X55),X56) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X83),X84),X85) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_com_Odistinct_I19_J) ).
thf(f1876,plain,
spl102_50,
inference(avatar_split_clause,[],[f969,f1874]) ).
thf(f1874,plain,
( spl102_50
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK43,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_50])]) ).
thf(f969,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK43,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f790]) ).
thf(f790,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK43,X0))) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f621,f789]) ).
thf(f789,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK43,X0))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f621,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f620]) ).
thf(f620,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f314]) ).
thf(f314,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( $true = vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
inference(fool_elimination,[],[f313]) ).
thf(f313,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))
=> vAPP(nat,$o,X0,X2) )
=> vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(rectify,[],[f143]) ).
thf(f143,axiom,
! [X29: nat > $o,X33: nat] :
( vAPP(nat,$o,X29,X33)
=> ( ! [X61: nat] :
( vAPP(nat,$o,X29,vAPP(nat,nat,suc,X61))
=> vAPP(nat,$o,X29,X61) )
=> vAPP(nat,$o,X29,zero_zero_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zero__induct) ).
thf(f1872,plain,
spl102_49,
inference(avatar_split_clause,[],[f960,f1870]) ).
thf(f1870,plain,
( spl102_49
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK33,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_49])]) ).
thf(f960,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK33,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f776]) ).
thf(f776,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK33,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK33,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f617,f775]) ).
thf(f775,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK33,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK33,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f617,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(flattening,[],[f616]) ).
thf(f616,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f310]) ).
thf(f310,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f309]) ).
thf(f309,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,zero_zero_nat)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
! [X29: nat > $o,X52: nat] :
( vAPP(nat,$o,X29,zero_zero_nat)
=> ( ! [X61: nat] :
( vAPP(nat,$o,X29,X61)
=> vAPP(nat,$o,X29,vAPP(nat,nat,suc,X61)) )
=> vAPP(nat,$o,X29,X52) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_nat__induct) ).
thf(f1868,plain,
spl102_48,
inference(avatar_split_clause,[],[f1566,f1866]) ).
thf(f1866,plain,
( spl102_48
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_48])]) ).
thf(f1566,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f1565]) ).
thf(f1565,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f1561]) ).
thf(f1561,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f929]) ).
thf(f929,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ),
inference(cnf_transformation,[],[f262]) ).
thf(f262,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
= ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_nat_Oinject) ).
thf(f1864,plain,
spl102_47,
inference(avatar_split_clause,[],[f958,f1862]) ).
thf(f1862,plain,
( spl102_47
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK32,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_47])]) ).
thf(f958,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK32,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f774]) ).
thf(f774,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK32,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK32,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f615,f773]) ).
thf(f773,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK32,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK32,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f615,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(flattening,[],[f614]) ).
thf(f614,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(ennf_transformation,[],[f308]) ).
thf(f308,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f307,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,zero_zero_nat)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f148]) ).
thf(f148,axiom,
! [X29: nat > $o,X2: nat] :
( vAPP(nat,$o,X29,zero_zero_nat)
=> ( ! [X120: nat] :
( vAPP(nat,$o,X29,X120)
=> vAPP(nat,$o,X29,vAPP(nat,nat,suc,X120)) )
=> vAPP(nat,$o,X29,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_old_Onat_Oinducts) ).
thf(f1860,plain,
spl102_46,
inference(avatar_split_clause,[],[f917,f1858]) ).
thf(f1858,plain,
( spl102_46
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,suc,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_46])]) ).
thf(f917,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f538]) ).
thf(f538,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f59]) ).
thf(f59,axiom,
! [X70: nat,X52: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X70),vAPP(nat,nat,suc,X52)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X70),X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_add__Suc__right) ).
thf(f1856,plain,
spl102_45,
inference(avatar_split_clause,[],[f916,f1854]) ).
thf(f1854,plain,
( spl102_45
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_45])]) ).
thf(f916,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X0)),X1) ),
inference(cnf_transformation,[],[f537]) ).
thf(f537,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X0)),X1) ),
inference(rectify,[],[f69]) ).
thf(f69,axiom,
! [X70: nat,X52: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X70),X52)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X70)),X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__Suc) ).
thf(f1852,plain,
spl102_44,
inference(avatar_split_clause,[],[f907,f1850]) ).
thf(f1850,plain,
( spl102_44
<=> ! [X0: list_char > int] : ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_44])]) ).
thf(f907,plain,
! [X0: list_char > int] : ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X0) ),
inference(cnf_transformation,[],[f255]) ).
thf(f255,plain,
! [X0: list_char > int] : ( $true = vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X0) ),
inference(fool_elimination,[],[f254]) ).
thf(f254,plain,
! [X0: list_char > int] : vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X0)),X0),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X12: list_char > int] : vAPP(sTfun(list_char,int),$o,vAPP(produc1260470173ar_int,sTfun(sTfun(list_char,int),$o),big_big_step,vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,skip),X12)),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Skip) ).
thf(f1847,plain,
spl102_43,
inference(avatar_split_clause,[],[f899,f1845]) ).
thf(f1845,plain,
( spl102_43
<=> ! [X0: set_Pr1148378109ar_int] : ( vAPP(sTfun(produc1260470173ar_int,$o),set_Pr1148378109ar_int,collec770796680ar_int,vAPP(set_Pr1148378109ar_int,sTfun(produc1260470173ar_int,$o),vAPP(sTfun(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o)),sTfun(set_Pr1148378109ar_int,sTfun(produc1260470173ar_int,$o)),cCOMB,member92250950ar_int),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_43])]) ).
thf(f899,plain,
! [X0: set_Pr1148378109ar_int] : ( vAPP(sTfun(produc1260470173ar_int,$o),set_Pr1148378109ar_int,collec770796680ar_int,vAPP(set_Pr1148378109ar_int,sTfun(produc1260470173ar_int,$o),vAPP(sTfun(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o)),sTfun(set_Pr1148378109ar_int,sTfun(produc1260470173ar_int,$o)),cCOMB,member92250950ar_int),X0)) = X0 ),
inference(cnf_transformation,[],[f253]) ).
thf(f253,plain,
! [X0: set_Pr1148378109ar_int] : ( vAPP(sTfun(produc1260470173ar_int,$o),set_Pr1148378109ar_int,collec770796680ar_int,vAPP(set_Pr1148378109ar_int,sTfun(produc1260470173ar_int,$o),vAPP(sTfun(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o)),sTfun(set_Pr1148378109ar_int,sTfun(produc1260470173ar_int,$o)),cCOMB,member92250950ar_int),X0)) = X0 ),
inference(fool_elimination,[],[f252]) ).
thf(f252,plain,
! [X0: set_Pr1148378109ar_int] :
( vAPP(sTfun(produc1260470173ar_int,$o),set_Pr1148378109ar_int,collec770796680ar_int,
^ [X1: produc1260470173ar_int] : vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X1),X0)) = X0 ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X48: set_Pr1148378109ar_int] :
( vAPP(sTfun(produc1260470173ar_int,$o),set_Pr1148378109ar_int,collec770796680ar_int,
^ [X49: produc1260470173ar_int] : vAPP(set_Pr1148378109ar_int,$o,vAPP(produc1260470173ar_int,sTfun(set_Pr1148378109ar_int,$o),member92250950ar_int,X49),X48)) = X48 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Collect__mem__eq) ).
thf(f1842,plain,
spl102_42,
inference(avatar_split_clause,[],[f1583,f1840]) ).
thf(f1840,plain,
( spl102_42
<=> ! [X1: list_typerep] : ( vAPP(nat,nat,suc,vAPP(list_typerep,nat,size_s416147576yperep,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_42])]) ).
thf(f1583,plain,
! [X1: list_typerep] : ( vAPP(nat,nat,suc,vAPP(list_typerep,nat,size_s416147576yperep,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(forward_demodulation,[],[f919,f915]) ).
thf(f915,plain,
! [X0: typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X1)) = vAPP(nat,nat,suc,vAPP(list_typerep,nat,size_s416147576yperep,X1)) ),
inference(cnf_transformation,[],[f536]) ).
thf(f536,plain,
! [X0: typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X1)) = vAPP(nat,nat,suc,vAPP(list_typerep,nat,size_s416147576yperep,X1)) ),
inference(rectify,[],[f190]) ).
thf(f190,axiom,
! [X53: typerep,X129: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X53),X129)) = vAPP(nat,nat,suc,vAPP(list_typerep,nat,size_s416147576yperep,X129)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_length__Cons) ).
thf(f919,plain,
! [X0: typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(cnf_transformation,[],[f540]) ).
thf(f540,plain,
! [X0: typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X1)),vAPP(nat,nat,suc,zero_zero_nat)) ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X116: typerep,X117: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X116),X117)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(list_typerep,nat,size_s416147576yperep,X117)),vAPP(nat,nat,suc,zero_zero_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_list_Osize_I4_J) ).
thf(f1838,plain,
spl102_41,
inference(avatar_split_clause,[],[f880,f1835]) ).
thf(f1835,plain,
( spl102_41
<=> ( relati186416454e_flip = cCOMB ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_41])]) ).
thf(f880,plain,
relati186416454e_flip = cCOMB,
inference(cnf_transformation,[],[f245]) ).
thf(f245,plain,
relati186416454e_flip = cCOMB,
inference(fool_elimination,[],[f244]) ).
thf(f244,plain,
( relati186416454e_flip
= ( ^ [X0: ( list_char > int ) > ( list_char > int ) > $o,X1: list_char > int,X2: list_char > int] : vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),X0,X2),X1) ) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
( relati186416454e_flip
= ( ^ [X35: ( list_char > int ) > ( list_char > int ) > $o,X19: list_char > int,X27: list_char > int] : vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),X35,X27),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_flip__def) ).
thf(f1833,plain,
spl102_40,
inference(avatar_split_clause,[],[f1564,f1831]) ).
thf(f1831,plain,
( spl102_40
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_40])]) ).
thf(f1564,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f1563]) ).
thf(f1563,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f1562]) ).
thf(f1562,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f929]) ).
thf(f1800,plain,
spl102_39,
inference(avatar_split_clause,[],[f970,f1798]) ).
thf(f1798,plain,
( spl102_39
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_39])]) ).
thf(f970,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero_nat) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f790]) ).
thf(f1796,plain,
spl102_38,
inference(avatar_split_clause,[],[f959,f1794]) ).
thf(f1794,plain,
( spl102_38
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK33,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_38])]) ).
thf(f959,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK33,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f776]) ).
thf(f1792,plain,
spl102_37,
inference(avatar_split_clause,[],[f957,f1790]) ).
thf(f1790,plain,
( spl102_37
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK32,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_37])]) ).
thf(f957,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK32,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero_nat) ) ),
inference(cnf_transformation,[],[f774]) ).
thf(f1788,plain,
spl102_36,
inference(avatar_split_clause,[],[f906,f1786]) ).
thf(f1786,plain,
( spl102_36
<=> ! [X0: produc1260470173ar_int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK21,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK22,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_36])]) ).
thf(f906,plain,
! [X0: produc1260470173ar_int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK21,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK22,X0)) = X0 ),
inference(cnf_transformation,[],[f762]) ).
thf(f762,plain,
! [X0: produc1260470173ar_int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK21,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK22,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f529,f761]) ).
thf(f761,plain,
! [X0: produc1260470173ar_int] :
( ? [X1: com,X2: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2) = X0 )
=> ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK21,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK22,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f529,plain,
! [X0: produc1260470173ar_int] :
? [X1: com,X2: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2) = X0 ),
inference(rectify,[],[f44]) ).
thf(f44,axiom,
! [X47: produc1260470173ar_int] :
? [X50: com,X51: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X50),X51) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_surj__pair) ).
thf(f1784,plain,
spl102_35,
inference(avatar_split_clause,[],[f904,f1782]) ).
thf(f1782,plain,
( spl102_35
<=> ! [X0: produc1260470173ar_int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK17,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK18,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_35])]) ).
thf(f904,plain,
! [X0: produc1260470173ar_int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK17,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK18,X0)) = X0 ),
inference(cnf_transformation,[],[f758]) ).
thf(f758,plain,
! [X0: produc1260470173ar_int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK17,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK18,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f603,f757]) ).
thf(f757,plain,
! [X0: produc1260470173ar_int] :
( ? [X1: com,X2: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2) = X0 )
=> ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,vAPP(produc1260470173ar_int,com,sK17,X0)),vAPP(produc1260470173ar_int,sTfun(list_char,int),sK18,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f603,plain,
! [X0: produc1260470173ar_int] :
? [X1: com,X2: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2) = X0 ),
inference(ennf_transformation,[],[f527]) ).
thf(f527,plain,
! [X0: produc1260470173ar_int] :
~ ! [X1: com,X2: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X1),X2) != X0 ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X46: produc1260470173ar_int] :
~ ! [X44: com,X45: list_char > int] : ( vAPP(sTfun(list_char,int),produc1260470173ar_int,vAPP(com,sTfun(sTfun(list_char,int),produc1260470173ar_int),produc1193801173ar_int,X44),X45) != X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_old_Oprod_Oexhaust) ).
thf(f1780,plain,
spl102_34,
inference(avatar_split_clause,[],[f915,f1778]) ).
thf(f1778,plain,
( spl102_34
<=> ! [X0: typerep,X1: list_typerep] : ( vAPP(list_typerep,nat,size_s416147576yperep,vAPP(list_typerep,list_typerep,vAPP(typerep,sTfun(list_typerep,list_typerep),cons_typerep,X0),X1)) = vAPP(nat,nat,suc,vAPP(list_typerep,nat,size_s416147576yperep,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_34])]) ).
thf(f1776,plain,
spl102_33,
inference(avatar_split_clause,[],[f1006,f1774]) ).
thf(f1774,plain,
( spl102_33
<=> ! [X2: com,X0: list_char,X1: aexp,X3: com] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_33])]) ).
thf(f1006,plain,
! [X2: com,X3: com,X0: list_char,X1: aexp] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X2),X3) ),
inference(cnf_transformation,[],[f574]) ).
thf(f574,plain,
! [X0: list_char,X1: aexp,X2: com,X3: com] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X2),X3) ),
inference(rectify,[],[f156]) ).
thf(f156,axiom,
! [X116: list_char,X117: aexp,X66: com,X67: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X66),X67) != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X116),X117) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_com_Odistinct_I9_J) ).
thf(f1772,plain,
spl102_32,
inference(avatar_split_clause,[],[f1005,f1770]) ).
thf(f1770,plain,
( spl102_32
<=> ! [X2: bexp,X0: com,X1: com,X3: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_32])]) ).
thf(f1005,plain,
! [X2: bexp,X3: com,X0: com,X1: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(cnf_transformation,[],[f573]) ).
thf(f573,plain,
! [X0: com,X1: com,X2: bexp,X3: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X66: com,X67: com,X55: bexp,X56: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X55),X56) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X66),X67) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_com_Odistinct_I17_J) ).
thf(f1768,plain,
spl102_31,
inference(avatar_split_clause,[],[f1004,f1766]) ).
thf(f1766,plain,
( spl102_31
<=> ! [X2: bexp,X0: list_char,X1: aexp,X3: com] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_31])]) ).
thf(f1004,plain,
! [X2: bexp,X3: com,X0: list_char,X1: aexp] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) ),
inference(cnf_transformation,[],[f572]) ).
thf(f572,plain,
! [X0: list_char,X1: aexp,X2: bexp,X3: com] : ( vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X116: list_char,X117: aexp,X55: bexp,X56: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X55),X56) != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X116),X117) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_com_Odistinct_I13_J) ).
thf(f1756,plain,
spl102_30,
inference(avatar_split_clause,[],[f965,f1754]) ).
thf(f1754,plain,
( spl102_30
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK38,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_30])]) ).
thf(f965,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK38,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f784]) ).
thf(f1752,plain,
spl102_29,
inference(avatar_split_clause,[],[f964,f1750]) ).
thf(f1750,plain,
( spl102_29
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK37,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_29])]) ).
thf(f964,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK37,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f784]) ).
thf(f1748,plain,
spl102_28,
inference(avatar_split_clause,[],[f962,f1746]) ).
thf(f1746,plain,
( spl102_28
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK36,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_28])]) ).
thf(f962,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK36,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f780]) ).
thf(f1744,plain,
spl102_27,
inference(avatar_split_clause,[],[f961,f1742]) ).
thf(f1742,plain,
( spl102_27
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK35,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_27])]) ).
thf(f961,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK35,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f780]) ).
thf(f1740,plain,
spl102_26,
inference(avatar_split_clause,[],[f882,f1737]) ).
thf(f1737,plain,
( spl102_26
<=> ( plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_26])]) ).
thf(f882,plain,
plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),
inference(cnf_transformation,[],[f249]) ).
thf(f249,plain,
plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),
inference(fool_elimination,[],[f248]) ).
thf(f248,plain,
( plus_plus_nat
= ( ^ [X0: nat,X1: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) ) ),
inference(rectify,[],[f109]) ).
thf(f109,axiom,
( plus_plus_nat
= ( ^ [X82: nat,X97: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X97),X82) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_add_Ocommute) ).
thf(f1735,plain,
( spl102_25
| ~ spl102_6
| ~ spl102_14 ),
inference(avatar_split_clause,[],[f1687,f1681,f1649,f1733]) ).
thf(f1733,plain,
( spl102_25
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK14,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_25])]) ).
thf(f1649,plain,
( spl102_6
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_6])]) ).
thf(f1681,plain,
( spl102_14
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_14])]) ).
thf(f1687,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK14,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl102_6
| ~ spl102_14 ),
inference(superposition,[],[f1650,f1682]) ).
thf(f1682,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl102_14 ),
inference(avatar_component_clause,[],[f1681]) ).
thf(f1650,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 )
| ~ spl102_6 ),
inference(avatar_component_clause,[],[f1649]) ).
thf(f1731,plain,
spl102_24,
inference(avatar_split_clause,[],[f972,f1729]) ).
thf(f1729,plain,
( spl102_24
<=> ! [X2: com,X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_24])]) ).
thf(f972,plain,
! [X2: com,X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) ),
inference(cnf_transformation,[],[f554]) ).
thf(f554,plain,
! [X0: bexp,X1: com,X2: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X83: bexp,X84: com,X85: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X83),X84),X85) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_com_Odistinct_I5_J) ).
thf(f1727,plain,
spl102_23,
inference(avatar_split_clause,[],[f905,f1725]) ).
thf(f1725,plain,
( spl102_23
<=> ! [X0: product_prod_nat_nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK19,X0)),vAPP(product_prod_nat_nat,nat,sK20,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_23])]) ).
thf(f905,plain,
! [X0: product_prod_nat_nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK19,X0)),vAPP(product_prod_nat_nat,nat,sK20,X0)) = X0 ),
inference(cnf_transformation,[],[f760]) ).
thf(f760,plain,
! [X0: product_prod_nat_nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK19,X0)),vAPP(product_prod_nat_nat,nat,sK20,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f528,f759]) ).
thf(f759,plain,
! [X0: product_prod_nat_nat] :
( ? [X1: nat,X2: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2) = X0 )
=> ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK19,X0)),vAPP(product_prod_nat_nat,nat,sK20,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f528,plain,
! [X0: product_prod_nat_nat] :
? [X1: nat,X2: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2) = X0 ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X47: product_prod_nat_nat] :
? [X50: nat,X51: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X50),X51) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_surj__pair) ).
thf(f1723,plain,
spl102_22,
inference(avatar_split_clause,[],[f903,f1721]) ).
thf(f1721,plain,
( spl102_22
<=> ! [X0: product_prod_nat_nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK15,X0)),vAPP(product_prod_nat_nat,nat,sK16,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_22])]) ).
thf(f903,plain,
! [X0: product_prod_nat_nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK15,X0)),vAPP(product_prod_nat_nat,nat,sK16,X0)) = X0 ),
inference(cnf_transformation,[],[f756]) ).
thf(f756,plain,
! [X0: product_prod_nat_nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK15,X0)),vAPP(product_prod_nat_nat,nat,sK16,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f602,f755]) ).
thf(f755,plain,
! [X0: product_prod_nat_nat] :
( ? [X1: nat,X2: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2) = X0 )
=> ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,vAPP(product_prod_nat_nat,nat,sK15,X0)),vAPP(product_prod_nat_nat,nat,sK16,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f602,plain,
! [X0: product_prod_nat_nat] :
? [X1: nat,X2: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2) = X0 ),
inference(ennf_transformation,[],[f526]) ).
thf(f526,plain,
! [X0: product_prod_nat_nat] :
~ ! [X1: nat,X2: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X1),X2) != X0 ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
! [X46: product_prod_nat_nat] :
~ ! [X44: nat,X45: nat] : ( vAPP(nat,product_prod_nat_nat,vAPP(nat,sTfun(nat,product_prod_nat_nat),product_Pair_nat_nat,X44),X45) != X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_old_Oprod_Oexhaust) ).
thf(f1719,plain,
spl102_21,
inference(avatar_split_clause,[],[f1136,f1716]) ).
thf(f1716,plain,
( spl102_21
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,ua),t_a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_21])]) ).
thf(f1136,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,ua),t_a) = $true,
inference(cnf_transformation,[],[f488]) ).
thf(f488,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,ua),t_a) = $true,
inference(fool_elimination,[],[f487]) ).
thf(f487,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,ua),t_a),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,ua),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Suc_Oprems_I5_J) ).
thf(f1714,plain,
spl102_20,
inference(avatar_split_clause,[],[f1135,f1711]) ).
thf(f1711,plain,
( spl102_20
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,u),t) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_20])]) ).
thf(f1135,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,u),t) = $true,
inference(cnf_transformation,[],[f486]) ).
thf(f486,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,u),t) = $true,
inference(fool_elimination,[],[f485]) ).
thf(f485,plain,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,u),t),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(sTfun(list_char,int),sTfun(sTfun(list_char,int),$o),q,u),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062Q_Au_____At_H_____092_060close_062) ).
thf(f1709,plain,
( spl102_19
| ~ spl102_6
| ~ spl102_13 ),
inference(avatar_split_clause,[],[f1685,f1677,f1649,f1707]) ).
thf(f1707,plain,
( spl102_19
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK13,X0) != X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_19])]) ).
thf(f1677,plain,
( spl102_13
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero_nat = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_13])]) ).
thf(f1685,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK13,X0) != X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl102_6
| ~ spl102_13 ),
inference(superposition,[],[f1650,f1678]) ).
thf(f1678,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero_nat = X0 ) )
| ~ spl102_13 ),
inference(avatar_component_clause,[],[f1677]) ).
thf(f1705,plain,
spl102_18,
inference(avatar_split_clause,[],[f1134,f1702]) ).
thf(f1134,plain,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa) = $true,
inference(cnf_transformation,[],[f484]) ).
thf(f484,plain,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa) = $true,
inference(fool_elimination,[],[f483]) ).
thf(f483,plain,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),sa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Suc_Oprems_I6_J) ).
thf(f1700,plain,
spl102_17,
inference(avatar_split_clause,[],[f1133,f1697]) ).
thf(f1697,plain,
( spl102_17
<=> ( vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),s2) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_17])]) ).
thf(f1133,plain,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),s2) = $true,
inference(cnf_transformation,[],[f482]) ).
thf(f482,plain,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),s2) = $true,
inference(fool_elimination,[],[f481]) ).
thf(f481,plain,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),s2),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(sTfun(list_char,int),$o,vAPP(bexp,sTfun(sTfun(list_char,int),$o),bval,b),s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062bval_Ab_As_____092_060close_062) ).
thf(f1695,plain,
spl102_16,
inference(avatar_split_clause,[],[f913,f1693]) ).
thf(f1693,plain,
( spl102_16
<=> ! [X0: list_char,X1: aexp] : ( zero_zero_nat = vAPP(com,nat,size_size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_16])]) ).
thf(f913,plain,
! [X0: list_char,X1: aexp] : ( zero_zero_nat = vAPP(com,nat,size_size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1)) ),
inference(cnf_transformation,[],[f534]) ).
thf(f534,plain,
! [X0: list_char,X1: aexp] : ( zero_zero_nat = vAPP(com,nat,size_size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1)) ),
inference(rectify,[],[f169]) ).
thf(f169,axiom,
! [X116: list_char,X117: aexp] : ( zero_zero_nat = vAPP(com,nat,size_size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X116),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_com_Osize_I7_J) ).
thf(f1691,plain,
spl102_15,
inference(avatar_split_clause,[],[f912,f1689]) ).
thf(f1689,plain,
( spl102_15
<=> ! [X0: list_char,X1: aexp] : ( zero_zero_nat = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_15])]) ).
thf(f912,plain,
! [X0: list_char,X1: aexp] : ( zero_zero_nat = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1)) ),
inference(cnf_transformation,[],[f533]) ).
thf(f533,plain,
! [X0: list_char,X1: aexp] : ( zero_zero_nat = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1)) ),
inference(rectify,[],[f171]) ).
thf(f171,axiom,
! [X116: list_char,X117: aexp] : ( zero_zero_nat = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X116),X117)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_com_Osize__gen_I2_J) ).
thf(f1683,plain,
spl102_14,
inference(avatar_split_clause,[],[f902,f1681]) ).
thf(f902,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f754]) ).
thf(f754,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f601,f753]) ).
thf(f753,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f601,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f525]) ).
thf(f525,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X52: nat] :
( ( zero_zero_nat != X52 )
=> ? [X121: nat] : ( vAPP(nat,nat,suc,X121) = X52 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_not0__implies__Suc) ).
thf(f1679,plain,
spl102_13,
inference(avatar_split_clause,[],[f901,f1677]) ).
thf(f901,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(cnf_transformation,[],[f752]) ).
thf(f752,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f600,f751]) ).
thf(f751,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f600,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero_nat = X0 ) ),
inference(ennf_transformation,[],[f524]) ).
thf(f524,plain,
! [X0: nat] :
( ( zero_zero_nat != X0 )
=> ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X46: nat] :
( ( zero_zero_nat != X46 )
=> ~ ! [X120: nat] : ( vAPP(nat,nat,suc,X120) != X46 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_old_Onat_Oexhaust) ).
thf(f1675,plain,
spl102_12,
inference(avatar_split_clause,[],[f911,f1673]) ).
thf(f1673,plain,
( spl102_12
<=> ! [X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_12])]) ).
thf(f911,plain,
! [X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1) ),
inference(cnf_transformation,[],[f532]) ).
thf(f532,plain,
! [X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
! [X55: bexp,X56: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X55),X56) != skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_com_Odistinct_I7_J) ).
thf(f1671,plain,
spl102_11,
inference(avatar_split_clause,[],[f910,f1669]) ).
thf(f1669,plain,
( spl102_11
<=> ! [X0: com,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_11])]) ).
thf(f910,plain,
! [X0: com,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(cnf_transformation,[],[f531]) ).
thf(f531,plain,
! [X0: com,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X66: com,X67: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X66),X67) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_com_Odistinct_I3_J) ).
thf(f1667,plain,
spl102_10,
inference(avatar_split_clause,[],[f909,f1665]) ).
thf(f1665,plain,
( spl102_10
<=> ! [X0: list_char,X1: aexp] : ( skip != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_10])]) ).
thf(f909,plain,
! [X0: list_char,X1: aexp] : ( skip != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) ),
inference(cnf_transformation,[],[f530]) ).
thf(f530,plain,
! [X0: list_char,X1: aexp] : ( skip != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X0),X1) ),
inference(rectify,[],[f155]) ).
thf(f155,axiom,
! [X116: list_char,X117: aexp] : ( skip != vAPP(aexp,com,vAPP(list_char,sTfun(aexp,com),assign,X116),X117) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_com_Odistinct_I1_J) ).
thf(f1663,plain,
spl102_9,
inference(avatar_split_clause,[],[f894,f1661]) ).
thf(f1661,plain,
( spl102_9
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),zero_zero_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_9])]) ).
thf(f894,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),zero_zero_nat) = X0 ),
inference(cnf_transformation,[],[f519]) ).
thf(f519,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),zero_zero_nat) = X0 ),
inference(rectify,[],[f175]) ).
thf(f175,axiom,
! [X6: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X6),zero_zero_nat) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_verit__sum__simplify) ).
thf(f1659,plain,
spl102_8,
inference(avatar_split_clause,[],[f891,f1657]) ).
thf(f1657,plain,
( spl102_8
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_8])]) ).
thf(f891,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X0) = X0 ),
inference(cnf_transformation,[],[f516]) ).
thf(f516,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X0) = X0 ),
inference(rectify,[],[f124]) ).
thf(f124,axiom,
! [X6: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,zero_zero_nat),X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add_Oleft__neutral) ).
thf(f1655,plain,
spl102_7,
inference(avatar_split_clause,[],[f885,f1653]) ).
thf(f1653,plain,
( spl102_7
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != zero_zero_nat ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_7])]) ).
thf(f885,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != zero_zero_nat ),
inference(cnf_transformation,[],[f511]) ).
thf(f511,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != zero_zero_nat ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X70: nat] : ( vAPP(nat,nat,suc,X70) != zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Zero__not__Suc) ).
thf(f1651,plain,
spl102_6,
inference(avatar_split_clause,[],[f884,f1649]) ).
thf(f884,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(cnf_transformation,[],[f510]) ).
thf(f510,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(rectify,[],[f45]) ).
thf(f45,axiom,
! [X52: nat] : ( vAPP(nat,nat,suc,X52) != X52 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_n__not__Suc__n) ).
thf(f1647,plain,
spl102_5,
inference(avatar_split_clause,[],[f883,f1645]) ).
thf(f1645,plain,
( spl102_5
<=> ! [X0: typerep] : ( zero_zero_nat != vAPP(typerep,nat,size_size_typerep,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_5])]) ).
thf(f883,plain,
! [X0: typerep] : ( zero_zero_nat != vAPP(typerep,nat,size_size_typerep,X0) ),
inference(cnf_transformation,[],[f509]) ).
thf(f509,plain,
! [X0: typerep] : ( zero_zero_nat != vAPP(typerep,nat,size_size_typerep,X0) ),
inference(rectify,[],[f182]) ).
thf(f182,axiom,
! [X53: typerep] : ( zero_zero_nat != vAPP(typerep,nat,size_size_typerep,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_typerep_Osize__neq) ).
thf(f1643,plain,
spl102_4,
inference(avatar_split_clause,[],[f871,f1640]) ).
thf(f1640,plain,
( spl102_4
<=> ( zero_zero_nat = vAPP(com,nat,size_size_com,skip) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_4])]) ).
thf(f871,plain,
zero_zero_nat = vAPP(com,nat,size_size_com,skip),
inference(cnf_transformation,[],[f168]) ).
thf(f168,axiom,
zero_zero_nat = vAPP(com,nat,size_size_com,skip),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_com_Osize_I6_J) ).
thf(f1638,plain,
spl102_3,
inference(avatar_split_clause,[],[f870,f1635]) ).
thf(f1635,plain,
( spl102_3
<=> ( zero_zero_nat = vAPP(com,nat,size_com,skip) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_3])]) ).
thf(f870,plain,
zero_zero_nat = vAPP(com,nat,size_com,skip),
inference(cnf_transformation,[],[f170]) ).
thf(f170,axiom,
zero_zero_nat = vAPP(com,nat,size_com,skip),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_com_Osize__gen_I1_J) ).
thf(f1605,plain,
spl102_2,
inference(avatar_split_clause,[],[f225,f1603]) ).
thf(f1603,plain,
( spl102_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_2])]) ).
thf(f225,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1601,plain,
~ spl102_1,
inference(avatar_split_clause,[],[f224,f1598]) ).
thf(f1598,plain,
( spl102_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl102_1])]) ).
thf(f224,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : ITP166^1 : TPTP v8.1.2. Released v7.5.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 19:20:38 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (31297)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.35 % (31300)WARNING: value z3 for option sas not known
% 0.15/0.35 % (31302)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.35 % (31298)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.35 % (31301)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.35 % (31300)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.35 % (31303)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.35 % (31299)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.35 % (31304)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.41 % (31304)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.42 % Exception at run slice level
% 0.15/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.42 % Exception at run slice level
% 0.15/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.42 % Exception at run slice level
% 0.15/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.44 % (31307)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.44 % (31306)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.44 % (31308)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.49 % (31307)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.49 % (31306)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.50 % Exception at run slice level
% 0.15/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.52 % (31310)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.15/0.53 % (31302)First to succeed.
% 0.15/0.55 % (31302)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31297"
% 0.15/0.55 % (31302)Refutation found. Thanks to Tanya!
% 0.15/0.55 % SZS status Theorem for theBenchmark
% 0.15/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.60/0.56 % (31302)------------------------------
% 1.60/0.56 % (31302)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.60/0.56 % (31302)Termination reason: Refutation
% 1.60/0.56
% 1.60/0.56 % (31302)Memory used [KB]: 3671
% 1.60/0.56 % (31302)Time elapsed: 0.200 s
% 1.60/0.56 % (31302)Instructions burned: 487 (million)
% 1.60/0.56 % (31297)Success in time 0.236 s
%------------------------------------------------------------------------------